An EU referendum by the end of 2017 is among a packed programme of new laws in the first Conservative Queen's Speech in nearly two decades.
It also includes more free childcare, an income tax freeze and the right-to-buy for housing association tenants.
David Cameron said the 26-bill package was a "programme for working people" that would create full employment and "bring our country together".
The measures were unveiled by the Queen amid the usual pomp and ceremony.
The proposed legislation includes:
- A ban on income tax, VAT and national insurance increases for five years
- A freeze on working age benefits, tax credits and child benefit for two years from 2016/17
- 30 hours free childcare a week for three and four-year-olds by 2017
- Cutting the total amount one household can claim in benefits from £26,000 to £23,000
- More devolution for Scotland, Wales and Northern Ireland and "English votes for English laws" at Westminster
- 500 more free schools and more failing and "coasting" schools turned into Academies
- A ban on so-called legal highs
- A "truly seven day" NHS by 2020
- Here is a bill-by-bill rundown of the full programme. Follow all the action and the reaction in text and video on Politics Live
Many of the proposed new laws were promised by the Conservatives during the general election campaign and Mr Cameron can press ahead with plans previously blocked by the Liberal Democrats.
He told MPs that after the election, he now had a "clear mandate" from the British people and "we will not waste a single moment with getting on with the task," in his first speech to the new Parliament.
These include an Investigatory Powers Bill to give intelligence agencies new tools to target internet data, dubbed a "snooper's charter" by critics.
But the prime minister has delayed plans to scrap the Human Rights Act to avoid a potential confrontation with his own backbenchers. Instead, the government will bring forward proposals for a British Bill of Rights to replace the Human Rights Act, with legislation expected following consultation later in the parliament.
There was no mention in the speech of a promised free Commons vote on repealing the fox hunting ban, but environment secretary Liz Truss said the vote would happen by 2020.
Analysis by Political Correspondent Iain Watson
The political message is clear - that the government will help "working people" but not those claiming benefits who, in the words if the prime minister, are "sitting at home".
The Conservatives' own polling highlighted that this was a powerful message especially in the Midlands and southern marginals seized from, or defended from, Labour.
The intention is to try to recreate the coalition, not with the Lib Dems, but with people who don't traditionally back the Conservatives, but whose parents may well have voted for Mrs Thatcher before deserting the party for Tony Blair.
The prime minister is even using the language of 'One Nation' - briefly favoured by Ed Miliband.
Mr Cameron's flagship policy of giving 1.3 million housing association tenants in England the right to buy their homes at a discount was in the Queen's Speech.
Another key priority for the new government is Chancellor George Osborne's Northern Powerhouse plan, with a bill paving the way for HS2 and another piece of legislation enabling cities to bid for an elected mayor, with more powers over transport, planning, policing and health. The mayors would take over the role of Police and Crime Commissioner for their area.
There is also a Trade Unions Bill, imposing a 50% turnout threshold on strike ballots, with a further requirement in essential public services for strikes to be supported by 40% of those entitled to vote.
Reading out the speech, which is prepared for her by the government, from her throne in the House of Lords, the Queen said: "My government will legislate in the interests of everyone in the country.
"It will adopt a one nation approach, helping working people get on, supporting aspiration, giving new opportunities to the disadvantaged and bringing different parts of our country together."
Mr Cameron described his first legislative programme as the head of a Conservative government as an agenda for "working people," with three million more apprenticeships promised over the next five years and a new law to ensure the minimum wage remains tax free.
"There should be a job for everyone who wants one - in other words, full employment," said the prime minister in his introduction to the Queen's Speech.
'Bold first step'
He said that after the British economy was hauled back from the brink of disaster in 2010, the UK now stands "on the brink of something special".
"We have a golden opportunity to renew the idea that working people are backed in this country; to renew the promise to those least fortunate that they will have the opportunity for a brighter future; and to renew the ties that bind every part of our United Kingdom.
"We now have the mandate to deliver that renewal. And it starts with this Queen's Speech."
He described the programme as "the bold first step of a One Nation government".
Harriet Harman, Labour's acting leader, said her party would back the government's EU referendum bill but campaign for Britain to stay in the Union. She also confirmed that Labour had dropped its opposition to lowering the benefit cap.
She attacked proposals to give housing association tenants the right to buy their homes as "uncosted, unfunded and unworkable" and condemned plans to make it harder for workers to strike and other measures that "undermine people's rights at work" as "divisive posturing".
She also told Mr Cameron it would be "utterly irresponsible to continue what he did so shamefully in the general election which was to set the English against the Scottish," urging him not to give Scotland full fiscal autonomy demanded by the SNP.
The SNP said they were "the only real opposition to the Tories in Westminster", following a Queen's Speech which they said "ties Scotland to the wrong priorities".
But the party's 56 MPs got their first ticking off from Commons Speaker John Bercow when they burst into applause as their leader at Westminster Angus Robertson hit back at Labour MP Ian Austin, who angrily told them they should be sitting with the Conservatives.
The Speaker said the SNP members "must show some respect" for the Commons convention that frowns on applause.
In his speech, Mr Robertson called for "honesty" from the government on its plans for "austerity cuts".
"On the vow that was given to the people of Scotland, we will judge the Scotland Bill on its contents. The legislation that is introduced must live up to the Smith Commission in full, anything less would be a breach of faith," he added.
Former deputy prime minister Nick Clegg accused Mr Cameron of abandoning the "liberal stance" espoused by the previous coalition government.
In what he said would be his final Commons speech as Lib Dem leader, he told MPs: "The human rights we hold dear, our right to privacy in an online age, our future as an open-minded, outward-looking country, are all hanging in the balance again because of the measures announced today.
"It is clear, too, that the previous government's commitment to fairness is also weakened."
He began his speech, in a half empty chamber, by saying it was "an unaccustomed surprise" to speak in the Commons without being greeted by a "disobliging wall of noise" from the opposition benches.