A Eurosceptic Labour MP has launched a campaign against the EU constitution.
Mr Davidson wants a referendum
Ian Davidson told BBC Radio 4's Today that the group, Labour against a Superstate, wants a referendum held.
Nearly 60 Labour MPs already back the Vote 2004 campaign for a referendum - although that does not necessarily mean they oppose the constitution.
Tony Blair has rejected calls for a poll, but he will still have to ratify any constitution - now scheduled to be agreed in June - in Parliament.
Mr Davidson refused to be pinned down on how many of his Labour colleagues would support "Labour against a Superstate" and vote against the government.
He said he had "just started putting out feelers" but had been "very pleased by the number of folk who are indicating that they are supportive and encouraging us to continue campaigning".
"Labour against the euro," which was affiliated to the broader, UK-wide cross-party No Campaign, attracted the support of 37 Labour MPs.
But Mr Davidson claimed there was considerably more support behind the scenes, among anti-euro Labour MPs.
Tony Blair says the EU constitution will not lead to the type of fundamental changes which would require a referendum.
And he has promised not to give up the British veto on taxation, social security, foreign policy, defence and criminal justice.
Mr Davidson said the draft constitution, which EU leaders have set a deadline of 17 June to agree, will pave the way for greater centralisation of power.
"We want to have co-operation with Europe, but to be run by Europe," Mr Davidson told BBC Radio 4's Today programme.
"I believe that when Tony Blair listens to the party and the country and the people as a whole, he will recognise that there is overwhelming opposition to signing up to a new European constitution, which effectively would create a European superstate," he added.
There were reports last week that Tony Blair's advisers were considering a referendum in the autumn.
But rather than hold a vote on whether to accept the constitution the reports suggested it would ask whether Britain should remain in the European Union.
Echoing Tory objections to such a move, Mr Davidson said: "That is a distortion of the referendum process. That would be a false question".
"I think this is something that is just being floated in order to try and frighten people away from opposing the constitution," he added.
Pro-referendum supporter of Vote 2004, Lynne Jones, Labour MP for Birmingham Selly Oak, said: "I don't agree that the constitution is a bad thing for Britain, but I do agree that this issue is so important voters need to have a direct say.
"The government shouldn't be running scared of the voters - the debate has only just begun."