The government is set to unveil plans for a UK referendum on the EU constitution, the BBC has learned.
The treaty is due to be agreed by mid June
Tony Blair had always rejected holding a referendum on the treaty, due to be agreed by mid-June following the accession of 10 new EU members.
The BBC's political correspondent John Pienaar called the decision a major U-turn and a big change in policy.
Earlier, Conservative leader Michael Howard said Tony Blair must "stop playing games" on the issue.
The constitution will replace earlier European Union treaties with a single document saying what the EU can and cannot do.
It has been drawn up to streamline decision making, giving the EU a clearer sense of purpose that the public will understand more easily.
But critics of the treaty argue it is far more than the "tidying up" exercise ministers have suggested and will strengthen the powers of the EU.
Although the referendum, the first of its kind since 1975, has not been officially announced, the prime minister has taken the decision in principle.
Former trade union leader Sir Bill Morris, a senior campaigner for the pro-referendum group Vote 2004, told BBC News 24: "What we are being advised this evening is that the principal of a referendum is likely to be announced in the next few days and I think everyone should welcome that.
"It's an extension of our democratic process no less."
The hugely significant shift of policy follows months of resistance to holding a poll.
Pressure had been mounting from political opponents and a eurosceptic media who said the electorate should have a say on the issue.
The prime minister had argued the vote was not needed because the treaty would not alter Britain's relationship with the EU.
But on Saturday, Tony Blair told BBC Radio 4 that Conservative threats to renegotiate the treaty, if they were successful in the European elections, could trigger a poll.
"The thing that has changed recently is a radical change in the Conservative position, which is no longer to say they don't support this constitutional treaty, but they would re-negotiate it if it was passed," he told the Today programme.
Sunday newspapers had been predicting a decision would be made after pressure from senior colleagues.
But on Sunday the Deputy Prime Minister John Prescott told BBC Radio 4's The World This Weekend, Mr Blair was simply "listening to the argument" over the question of an EU poll.
Earlier, Mr Howard called on the prime minister "to trust the people and hold a referendum on the constitution...'yes or no'. We must decide this issue once and for all and not prolong the uncertainty."
He told the BBC a referendum could be held in the autumn, if agreement was reached at the EU treaty signing in June.
John Pienaar has said that Downing Street has reached the conclusion that the dangers of refusing a referendum outweigh the risks of calling one.
The EU will have ten new members
Labour was expected to suffer electorally, with the Conservatives plan to make a referendum on the constitution a central issue of their campaign for the European elections on 10 June.
The Liberal Democrats, who support the constitution, have also called for a referendum on the issue, and according to recent reports the Chancellor Gordon Brown has also swung in favour of consulting the electorate.
The announcement will possibly be made on Thursday, after a Cabinet meeting that will be asked to rubber stamp a decision that has already been discussed with ministers.
A poll could take place before the next general election, expected in around a year, a colleague of Gordon Brown has said in press reports.
Sir Menzies Campbell, Liberal Democrat foreign affairs spokesman, said: "If these reports are true they will represent an enormous volte-face on the part of the Government.
"But the opportunity must be taken to argue the case for Europe with both vigour and commitment.
The constitution has been drafted by the European Convention under the stewardship of former French President Valery Giscard d'Estaing, but member states have not been able to decide on a final agreement.