Prime Minister Gordon Brown has welcomed the agreement of a new EU treaty, reached after last-minute changes at a summit in Portugal.
Mr Brown said Britain's interests would be "protected" with opt-outs
"The red lines have been secured. The British national interest has been protected," Mr Brown said.
He said Britain can still set its own policies on justice, home and foreign affairs, as well as security.
But shadow Europe minister Mark Francois said the Conservatives would continue to campaign for a referendum.
Mr Brown said: "It is now time for Europe to move on and devote all our efforts to the issues that matter to the people of Europe - economic growth, jobs, climate change and security."
Earlier the European Commission's president Jose Manuel Barroso said Britain's requests for concessions in the EU treaty were likely to be met, but it must not make any fresh demands.
He added he hoped for no further "difficulties" at the two-day summit in Lisbon as he urged all EU leaders to back the treaty.
"We prefer to have a solution that is broadly agreed with some specific opt-outs for some countries than not to move forward," he had said.
Foreign Secretary David Miliband told BBC Radio 4's Today programme: "The consequence of this treaty is that Europe has to prove that it can make a real difference to people's lives on issues like climate change, jobs and terrorism."
The opt-outs, which Mr Brown referred to as "red lines", were in areas such as human rights, tax and benefits, foreign policy and justice.
The prime minister said that if these made the final draft of the treaty, it would avoid any significant transfer of power to Brussels.
Mr Barroso said a "broadly agreed" EU treaty would be a good outcome
"I've been determined that Britain will continue to decide in justice and home affairs - and I believe that the detailed changes that are being made with the opt-in for Britain in this area protect the British national interests," Mr Brown said at a news conference in the Portuguese capital before the deal was reached.
"On foreign affairs and security matters, it is important for us that Britain can decide, and that's why we have been determined that foreign policy remains inter-governmental and decisions are made by unanimity.
"On social security, we have been determined that there is an emergency break - and in some cases a veto - so that decisions are made in the interests of Britain."
Mr Brown, attending his first EU summit as prime minister, had pledged to veto the treaty if Britain's "red lines" were not fully incorporated.
Tory Mark Francois said: "In the small hours of the night Gordon Brown has agreed the revised EU constitution which potentially transfers massive powers from Britain to the EU.
"He had absolutely no democratic mandate to do this and we will now step up our campaign to secure the referendum which he promised the British people all along."
And shadow foreign secretary William Hague said that by failing to agree to a referendum, Mr Brown was "still treating the British people like fools" with comments that had "reached new depths of cynicism".
"He still claims that because the name 'constitution' has been dropped, this treaty is somehow different, even though the European Scrutiny Committee has specifically told him his argument is misleading.
"He claims that this treaty is about making a free-trading Europe work better, when he knows that it downgrades the importance of free competition."
But Mr Miliband said the constitution was "dead" and "by no measure" could the treaty be called a constitution.
He said it was time to dispel the "myths" that the treaty amounted to "the end of Britain".
Mr Hague said polls showed most British people wanted a referendum
'Country called Europe'
The UK Independence Party (UKIP) has also demanded a referendum, along with some Labour MPs, while ex-Lib Dem leader Sir Menzies Campbell has said a public vote should be held on the wider question of UK membership of the EU as well.
Speaking on BBC Radio 4, UKIP leader Nigel Farage said: "We've agreed a treaty that makes the European Union a country, a country called Europe now exists.
"Once this treaty goes through there's no legal debate or argument about that."
But Mr Brown was adamant a referendum was not needed.
"If we were debating as big an issue as Britain's membership of the euro, I would have been the first - indeed, I was the first - to say this is such an issue of great significance that the British people must vote in a referendum," he said.
"If it was the previous constitutional treaty, I would have argued, as we did, that there should have been a referendum. But this is an amending treaty, where the constitutional concept has been abandoned."
He said this was "a very different document" to the failed EU constitution, on which voters in the UK were promised a referendum.
And a parliamentary debate would be "the proper way of discussing this", he insisted, as long as the "red lines" made the final draft.