Prime Minister Boris Johnson has vowed to leave the EU "do or die" by the 31 October - the date the UK must depart if no deal has been reached.
But a government document outlining "reasonable worst case assumptions" in the event of such a no-deal Brexit has warned of rising food and fuel prices, disruption to medicine supplies and public disorder.
An extra £2.1bn of funding has been announced to help deal with the consequences of no deal.
How could you be affected if the UK does leave the EU without an agreement?
1. The contents of your shopping basket may change
What you find on the supermarket shelves could well be where you see the first effects.
Almost 30% of our food currently comes from the EU, and it is likely that some foods, such as fresh vegetables and fruit, will become more scarce and more expensive in the event of no deal.
The five-page document spelling out the government's worst-case assumptions under Operation Yellowhammer - the government's no-deal contingency plan - warns:
- Some fresh food supplies will decrease
- Key ingredients for food made in the UK may be in shorter supply
- There won't be a shortage of food overall, but there could be reduced availability and choice
- Prices may also increase "which could impact vulnerable groups"
Supermarkets themselves have warned that there could be empty shelves and higher prices.
In preparation, supermarkets say they have been stockpiling some foods - but they are unable to do that for some fresh fruit and veg.
Stockpiling is more of a challenge at this time of year too, businesses say, as warehouse capacity is already strained by the seasonal stock build-up ahead of Black Friday and Christmas.
The government has said it will continue to recognise EU standards for imported food, to minimise disruption.
It has also published a "tariff schedule", which has removed most tariffs on imports in the event of no deal.
Shoppers planning to buy from companies based in the EU, Norway, Liechtenstein and Iceland after a no-deal Brexit have also been warned credit and debit card charges may be higher and payments may take longer.
2. Electricity and gas prices may go up
Although there is not expected to be an immediate disruption to electricity or gas supplies, there are likely to be significant price rises for businesses and households, the government's Yellowhammer report warns.
The market price for electricity could climb because of a fall in the value of the pound against the euro, but also as a result of cutting ties with EU energy markets.
Yellowhammer warned this could mean that some energy firms "exit" the energy market, "exacerbating" the economic and political impact of Brexit.
The warnings echo the findings of a 2017 House of Lords report, which said the UK could be "more vulnerable to supply shortages in the event of extreme weather or unplanned generation outages" in the event of a no-deal Brexit.
46%UK domestic production
45%Imported via European pipelines, inc from Russia and Norway
8%Liquefied natural gas imports
The risk would arise as a result of the UK's exit from the EU's Internal Energy Market, it said.
The bulk of the UK's natural gas imports come via Norway, which is part of the Internal Energy Market, although it is not an EU member. But the government says trade in gas between the UK and Norway will continue in its current form regardless.
3. You will need to take extra measures when travelling to Europe
Millions of people from the UK travel abroad each year - the vast majority of journeys made to Europe.
If you are planning to make a journey to an EU member state after Brexit, the government is advising you to check you have the right paperwork.
Travel to Ireland will not change, even if there's no deal. You'll continue to be able to travel and work there in the same way as before.
The government is advising you to make sure your passport is valid for at least six months if you are travelling to most countries in Europe - the full list is here.
Until recently, UK citizens who renewed their passport before it expired could have up to nine months of the remaining validity added to their new travel document.
But the government has now warned that this time carried over may not count towards the six-month requirement after a no-deal Brexit. You can check if your passport has enough time left with this government tool.
You'll need to renew your passport before travelling if you do not have enough validity left. It usually takes three weeks.
You won't need a visa for stays of up to 90 days out of any 180-day period in the EU or Iceland, Liechtenstein, Norway and Switzerland (the European Economic Area). However, you may need a visa or permit to stay for longer, or to work or study.
When new rules are confirmed, information about visa requirements will be on each country's travel advice page.
The government has also advised that at EU borders you may need to:
- show a return or onward ticket
- show you have enough money for your stay
- use separate queueing lanes from EU, EEA and Swiss citizens
The government's Yellowhammer report also warns there may also be increased immigration checks at EU borders causing delays at airports and ports.
European health cover
In addition, if there is no deal, then in theory the cover provided by your European Health Insurance Card (EHIC) would cease to exist.
The government is advising travellers "whether there's a deal or not" to "get appropriate travel insurance with healthcare cover".
Ministers say it is "particularly important" to get travel insurance with the right cover if you have a pre-existing medical condition. This is because the EHIC scheme covers pre-existing conditions, while many travel insurance policies do not.
However you intend to travel, in the event of no-deal Brexit, the government says, you should check before you leave for any delays or disruption.
If you intend to drive in the EU, you'll need some extra documents:
- a "green card", which proves your insurance provides the minimum required cover (obtained from your vehicle insurance company)
- a GB sticker
- an International Driving Permit for some countries (you can check if you need one on the Post Office website)
The government says flights, ferries and cruises, the Eurostar and Eurotunnel and bus and coach services between the UK and the EU will continue to run as normal.
An earlier government assessment had warned of long queues at London's St Pancras International, the main Eurostar terminal in the UK, but Eurostar bosses have said they are working to ensure their services run as smoothly as possible.
However, the government does warn some bus and coach services to non-EU countries, such as Switzerland or Andorra, may not be able to run.
After Brexit you will not be able to use the existing pet passport scheme and will instead need to follow a different process, involving a number of vet's tests. The process could take up to four months.
If you have a UK bank account and intend to use your bank card to pay for goods and services while you are in the EU as well as Iceland, Liechtenstein and Norway, the government has warned that it may become more expensive.
4. You may need to check medication is available and it may be more expensive
While there are regular fluctuations in medicine supplies, there are concerns a no-deal Brexit could make shortages worse.
The government's Yellowhammer document warns supplies of medicines and medical products are "particularly vulnerable" to disruption at Channel ports. While some products can be stockpiled, others can't because of their short shelf life, it says.
More than 12,000 medicines are used by the NHS, and about 7,000 come from or via the EU.
Ministers and NHS leaders say every effort is being made to ensure there will be enough medicines and clinical equipment available in the event of delays to imports from the EU.
The government has announced a further £434m of funding and other measures, including:
- extra warehouse space for medicines
- securing additional roll-on, roll-off freight capacity in ports away from Dover and Folkestone
- building buffer stocks
- booking plane space for products requiring immediate shipment
- making changes to regulatory requirements
- strengthening processes to deal with shortages
However, the National Audit Office has said there are still "significant" gaps in the government's preparation regarding the NHS and care homes.
5. UK nationals living abroad may have to take extra measures
About 1.3 million UK-born people live in the other 27 EU countries.
The UK government has requested that EU countries reciprocate its promise to uphold the rights of EU citizens in the UK, meaning UK citizens living in the EU would be able to continue their lives broadly as now.
In event of no deal, this would ensure they would have continued access to employment, healthcare, education, benefits and other services.
However, the government's Yellowhammer document warns that as UK nationals will lose their EU citizenship, they can "expect to lose associated rights and access to services over time".
The government has announced a public information campaign and an increase in consular support for Britons living abroad, costing £138m.
It advises UK citizens living in the EU to subscribe to updates from the relevant country advice pages.
UK nationals living in, working in, or visiting the EU may find their access to healthcare in EU member states will change after the UK leaves the EU with no deal. This will depend on decisions made by each country.
However, the UK government says it is seeking bilateral agreements to maintain healthcare rights, as a top priority.
Its Yellowhammer report warns that while EU countries should treat people with urgent needs, they may be required to pay. This could mean some people facing "substantial costs".
Information on how to access healthcare abroad can be found on the NHS website.
The UK government will continue to pay state pension, child benefits, and disability benefits to eligible UK nationals in the EU.
The UK's exit from the EU will not change existing double taxation arrangements, which apply to EU countries.
These ensure everyone - not just British citizens - living in a country that has a treaty with the UK will not pay tax in two countries on the same income or gain - and determine which country has primary taxing rights.
UK nationals who live in the EU, European Economic Area or Switzerland should swap their UK driving licences for a local licence before 31 October 2019. If there is no deal, licence exchange arrangements may stop and UK licence holders may have to retake their driving test in the country where they live.
6. EU citizens need to apply for 'settled status'
The UK government has reached an agreement with the EU, as well as Norway, Iceland, Liechtenstein, and Switzerland, that will protect the rights of EU citizens and their family members living in the UK.
There are currently 2.37 million EU nationals working in Britain, according to the Office of National Statistics (ONS).
The ONS has revised its estimates for overall arrivals to the UK - both from the EU and the rest of the world. Those new figures show the number of people arriving from the EU had been rising before the referendum.
Statisticians have not yet adjusted the figures for EU immigration after 2016, but unrevised figures showed a steep decline.
If you are an EU citizen and living in the UK, the government has a tool to find out what you need to do and when.
Home Office minister Brandon Lewis has warned that the UK will deport EU citizens after Brexit if they do not apply for the right to remain in time.
7. Importing goods from the EU may get more expensive
Importing goods from the EU is likely to get more expensive when free movement of goods ends with the UK's departure.
As a member of the EU, UK firms don't have to pay extra duties, taxes or have customs checks on goods travelling to or from the EU.
But after a no-deal Brexit, new rules will apply. UK businesses will need to apply the same processes to EU trade that apply when trading with the rest of the world.
Individuals may also have to pay VAT, duty and fees if they receive parcels worth more than £135.
A tariff is a tax applied to goods that are traded on international markets. Mostly, they are applied to imported goods by the country importing them. But there can also be tariffs on exported goods.
Under the temporary scheme, 88% of imports by value would be eligible for zero-tariff access. At the moment, 80% of imports are tariff free.
Tariffs would be maintained to protect some industries, including agriculture. Beef, lamb, poultry and some dairy products would receive protection.
8. House prices could be affected
Most commentators and industry experts agree uncertainty created by the Brexit process is causing buyers and sellers to sit tight, causing a slowdown in the housing market.
UK house prices rose at a slower rate in the year to July than at any time since September 2012, according to the Office of National Statistics.
Brexit uncertainty meant key aspects of the housing market were "pretty much flatlining", the Royal Institution of Chartered Surveyors has said.
The Bank of England says the impact of the UK leaving the EU on the housing market could be significant.
It has said house prices could fall by up to 30% from pre-Brexit levels if there was no deal, or a "disorderly Brexit". In July, the Office for Budget responsibility estimated a possible 10% fall in house prices by 2021 in the event of no-deal.
But bad news for homeowners might be better news for first time buyers trying to get a foot on the property ladder.
9. Some ports and motorways could see extra delays
Up to 85% of lorries using the main channel crossings "may not be ready" for French customs and could face queues of two-and-a-half days, the government's Yellowhammer report warns.
These queues at Channel ports could reduce the flow of trucks to 40-60% of current levels within a day, it says, with the worst disruption lasting up to three months.
Even after that time, traffic flows may only reach 50-70% of current levels and delays could lead to queues in Kent and other routes to France for significantly longer, the report said.
Remind yourself of the Brexit basics with:
In the event of bottlenecks, a traffic management system known as Operation Brock would come into force on a section of the M20. Traffic would be allowed to flow in both directions on the same carriageway, while lorries would be left queuing on the other side.
If that proved to be insufficient, a disused airfield near Ramsgate would be used as a lorry park, and if further capacity was still required, the M26 could also be used.
Kent County Council says it has employed extra staff and stockpiled supplies in preparation for six months of disruption in the event of no deal.
To ensure more lorries are ready for customs, the government announced last month that 88,000 companies would be automatically enrolled in a new customs system.
The government has also announced £344m more funding to be spent on new border and customs operations.
10. UK students studying in the EU and EU students studying in the UK face a period of uncertainty
More than 16,000 British students studied on placements organised by the Erasmus study abroad scheme - in place since the 1980s - in 2016-17.
UK universities say they would expect a similar number to be planning to do the same this coming academic year.
The government and the EU have agreed that people who have already started Erasmus trips will be able to continue them.
This is true for both UK students planning to go to EU countries, and EU nationals hoping to come to the UK.
The government has also issued a "guarantee" that funding will be available to UK organisations who have had Erasmus applications approved by the European Commission at the time the UK departs, but which have not yet begun.
Institutions are being advised to apply for this "HMG guarantee" to ensure they get the funding.
Meanwhile, Universities UK has launched a campaign supporting opportunities for studying abroad.
By Lucy Rodgers, Mike Hills and Dominic Bailey.