The Government could face a fresh revolt over the controversial European Arrest Warrant (EAW) after Labour said it will force a vote on the measure next week.
The move follows chaotic scenes in the Commons which resulted in the Government receiving the backing of MPs for opting into a package of European Union policing and criminal justice measures but only after hours of bitter wrangling.
The Opposition's decision to force a vote on the issue on November 19 could deepen Tory divisions on Europe on the eve of the Rochester and Strood by-election.
Labour said a vote explicitly on the EAW was necessary to give legal certainty following the Commons process followed by the Government which was condemned by senior MPs.
It is "important that Parliament's view is clearly given on the EAW to avoid legal challenges, given the chaos of yesterday", a source said.
Debate on the Government motion last night - a draft of the Criminal Justice and Data Protection (Protocol No 36) Regulation - was cut short after shadow home secretary Yvette Cooper used a rare procedural device to attempt to postpone a decision until the EAW could be properly considered.
Cooper's move failed but was still enough to curtail debate by forcing the main vote to take place almost two hours early, despite filibustering from Tory MPs.
David Cameron was forced to return early from the Lord Mayor's Banquet to take part in the vote, as did Chancellor George Osborne and other MPs.
David Cameron speaks to an aide during the Lord Mayor's Banquet
The highly unorthodox scenes were a final act to a dramatic series of major rows in the Commons chamber.
The clashes blew up with little warning after it emerged that the Government's motion referred only to 11 of 35 measures which the Government planned to opt into, with the EAW not included in the group being voted on.
Speaker John Bercow confirmed to MPs they were not voting on the EAW and blasted the Government for trying to "slip things through".
He told the Commons: "I think I have given a fairly clear indication that this has been a rather sorry saga and the House should not be put in this position.
"I think most of us think a commitment made is a commitment that should be honoured and we should try to operate according to sensible standards rather than trying to slip things through through some sort of artifice.
"It may be the sort of thing that some people think is very clever, but people outside of the House expect straightforward dealing and they are, frankly, contemptuous -and I use the word advisedly - contemptuous of what is not straight dealing. Let's try to learn from this experience and do better."
The Speaker told MPs he had spoken to "disinterested experts" and studied the motion before coming to the view that the vote was not on the EAW.
Conservative Sir Richard Shepherd said the Government "seemed sly" as a result of the situation.
European Scrutiny Committee chair Bill Cash described the situation as a trick that was "tainted with chicanery" and "completely unbelievable".
May insisted the Government regarded the vote as the Commons verdict on the whole package, despite Bercow's ruling that the EAW was not the subject of the day's debate or vote.
Labour's motion hoping to postpone the debate was defeated 272 to 229, majority 43, before the Government, with Opposition support, saw its original motion carried by 464 to 38, majority 426.
There were 25 Tory backers for Cooper's motion, while there were 36 Conservative rebels in the main division, plus a Tory teller.
May accused Labour of "playing politics" with the issue.
But Cooper claimed May was "playing fast and loose with the criminal justice system" and told her: "You have effectively said ministers are just going to make it up because the Speaker has been very clear that this does not include a vote on the EAW, you are just going to reinterpret it in any way you choose. That is an irresponsible way to treat the House."
May, who spoke for almost 30 minutes as MPs and whips assembled, said: "We have debated the EAW, had you not moved your motion other members of this House would have been able to debate the EAW, but I have to say in relation to the motion you have put, I would say to MPs this is not an attempt to ensure this House has a proper debate, it is not an attempt to ensure this House takes a vote on these important measures.
"I have made clear I think we should be able to continue this debate. I think it is quite wrong for you to have called this motion in the way you have done this evening and I would hope MPs would vote against it."
Government MPs staged a filibuster to give time for their colleagues to return to the Commons, but several spoke out against the Government and backed Ms Cooper.
In the day's earlier debate about the procedures followed by the Government, May said the Government was treating the vote on the group of 11 measures as the Commons verdict on the whole package of 35.
She said: "The vote on the next motion will be a vote on the regulations, which includes within it those measures a package of 35 we wish to opt back into which require to be transposed into UK legislation.
"But the Government is clear we will be bound by that vote and if this House chooses not to transpose those measures and votes against the regulation, then it will be voting against the Government opting into all of the measures, including the EAW."
Tory former Cabinet minister Liam Fox said Bercow had gone "over the top" but acknowledged it would have been "easier" for the Government to have allowed MPs to vote specifically on the EAW.
Fox said: "I think it would have been better for all concerned if the Government had simply put down an adjournment motion and debated the European Arrest Warrant in itself."
He said ministers were "technically correct" in the procedure they had followed "but I think the House was angry because the House wanted a specific debate on a specific issue".
"It would have been easier to give them that," he told the BBC Radio 4 Today programme.
But he accused Labour of "synthetic anger" where "the needle was going off the hypocrisy scale".
Asked if the Speaker had gone "over the top", Fox said: "I think everybody went over the top a little bit. It wasn't the best day I've been in in Parliament.
"But there's is no doubt the Government were technically correct but I think they misjudged the mood of the House. I think the Speaker possibly did go over the top and the Labour Party's cant and hypocrisy knew no bounds."Suggest a correction