The government has temporarily relaxed the legal restrictions on the length of time lorry drivers can work to help ease the backlog caused by snow.
Transport Secretary Philip Hammond said allowing hauliers to drive for an extra hour a day for the next four days would help deliveries of "vital supplies".
Royal Mail reported problems with about 10% of deliveries on Friday, and pumps at hundreds of garages could run dry.
Forecasters are warning freezing conditions could continue next week.
There are Met Office warnings of icy roads covering much of the UK, while Saturday's sporting fixtures also hit, with all Scottish Premier League football cancelled while rugby union and horse racing has been affected.
Seven people have also died in weather-related incidents.
Two men, aged 30 and 56 and both from Nottinghamshire, were killed in a motorway crash on the M62 in Humberside on Friday morning after their pick-up truck was in a collision with a lorry.
Humberside police said the lorry driver, a 36-year-old Manchester man, was arrested on suspicion of causing death by dangerous driving.
Grace Simpson and Jessica Lakin, both 19, were killed in a crash involving their car and a Royal Mail van on the A595 in Carlisle on Thursday. A Cumbria police spokesman said the treacherous road conditions "appeared to have been a factor".
Police in Cumbria are also investigating the deaths of two elderly people - 80-year-old Lillian Jenkinson from Workington and 84-year-old William Wilson from Waitby, near Kirkby - who died in their gardens in freezing conditions in separate incidents.
A 57-year-old man who went to the aid of a driver whose car had crashed in Bellerby, North Yorkshire, on Thursday, died after he was hit by another vehicle.
Announcing the temporary driving relaxation - which has increased the daily driving limit from nine to 10 hours - Mr Hammond said: "During these exceptional conditions we must do everything we can to keep Britain moving.
"That is why I have authorised a temporary relaxation of drivers' hours and working time rules for all HGV drivers over the next four days. This will ensure that vital supplies get to their destination on time."
The Federation of Petroleum Suppliers, which represents the majority of oil distribution companies in Britain, weclomed the relaxation, saying it would help distributors catch up with any backlog of orders.
A Downing Street spokesman said there were no major concerns over supplies of food, petrol, diesel or gas.
Brian Madderson, chairman of the Independent Petrol Retailers Association, said the relaxation should stop shortages on forecourts this weekend, but warned that crude oil prices had hit an all time high, and that the weather would push up petrol prices.
"Over the next two or three weeks the cost of product is definitely going to go up and this is being said by the fuel analysts, largely due to the wintry weather on the continent of Europe which is pushing up demand for heating oil," he said.
Paul Tollhurst, operations director at Royal Mail, said two million households received no mail at all on Friday but the improvement in weather had meant it could "start pumping mail through" on Saturday.
"We are taking on additional trucks and indeed we've got some extra train services running both northbound out of London towards Glasgow and up the East Coast mainline towards Newcastle," he said.
Extra staff have also been taken on as this is traditionally the busiest weekend for online trading before Christmas, he added.
Temperatures are expected to rise above freezing during daytime this weekend, although further heavy snow is likely in northern Scotland over the weekend.
Heavy rain along the coast of south-east England, combined with snow melt, could cause surface flooding later on Saturday, warned BBC forecaster Alex Deakin.
Dry and bright conditions are expected on Sunday, he said.
Severe weather warnings of widespread ice have been issued for the Highlands and Eilean Siar, Orkney and Shetland, Grampian, Northern Ireland, Wales, north-west England, Yorkshire and Humber, West Midlands, East Midlands and East of England.
There are warnings about an ongoing risk of widespread icy stretches across most of the UK, especially on Saturday evening and overnight.
Some trains have been restored to the north of Scotland after snow virtually wiped out services beyond the central belt on Friday.
But Northern Rail said the aftermath of the severe weather continues to affect some train services in Yorkshire and Humberside and the North East, with a number of routes not running on Sunday
ScotRail says there is a reduced service between Aberdeen and Inverness and Edinburgh and Inverness, and buses will replace trains between Glasgow and Aberdeen. The service between Edinburgh and Aberdeen has also been suspended.
The heavy snowfall has benefited Scotland's ski centres, with the Nevis Range enjoying its earliest start to a season for 13 years.
However, walkers, skiers and climbers have been urged to watch out for avalanches and plan their routes carefully as they take to Scotland's mountains this weekend.
The RAC said after receiving nearly 15,000 calls on Friday and nearly 140,000 since the start of the bad weather, it had been a relatively quiet Saturday morning. Wales was the busiest area due to icy roads.
A spokesman said: "Drivers are advised to check out local road and weather conditions before setting out as, despite the apparent improved weather in many parts of the country, many roads are still treacherous.
"And with temperatures falling later in the day drivers can expect to see widespread icy conditions."
The AA said it had attended about 17,500 breakdowns across the UK up to 1700 GMT on Friday - up from about 16,000 on Thursday. A typical Friday, normally the organisation's quietest day, brings about 9,500 call-outs. The busiest areas were Glasgow, Edinburgh, Newcastle, Leeds and Bradford.
Eurostar cancelled 17 trips on Friday and said its timetable would be significantly reduced, with cancellations and delays, until Sunday.
Gatwick Airport has reopened after being shut for two days but is warning passengers to expect delays and cancellations as it takes a few days for schedules to return to normal.
Passengers are being told to check with their airline before leaving home.
Robin Hood Airport, in Doncaster, will remain closed until 1000 GMT on Monday.