Rebels are demanding the Government go further in making clear that MPs and peers will have a vote, not only to approve any deal agreed with the EU, but also to decide whether the UK leaves the bloc with no deal if one cannot be agreed.
On Monday the House of Commons will vote on the matter and Tory backbenchers are saying Ms May must be clearer in her guarantees to give Parliament a say on the final Brexit deal if she wants to avoid an embarrassing defeat.
It comes after the Government’s attempt to avoid a rebellion over plans to increase National Insurance contributions on self-employed people, revealing the difficulty of Ms May’s position in passing controversial legislation with only the slimmest of Commons majorities.
Ex-cabinet minister Nicky Morgan MP told The Independent: “The Government needs to address how Parliament has a say in the event no agreement can be reached with the EU.
“Our constituents will expect us to have a say and that is the bit of the Lords amendment the Government has not yet publicly addressed.”
Ms May is currently trying to pass her Article 50 Bill through Parliament, which when written into law will give her the power to trigger Brexit talks.
She and her ministers had demanded the legislation be passed unapproved, but the House of Lords backed amendments to guarantee the rights of EU citizens living in the UK and to guarantee Parliament a vote on whatever happens at the end of Brexit negotiations.
The Labour party, which was behind the so-called “meaningful vote” amendment, is also pushing for greater assurances from the Government.
The Prime Minister had originally said that she would only allow MPs a vote on the terms of the deal she agrees with the EU, and threatened to leave the bloc with no deal if Parliament rejects them.
But concerned Conservative backbenchers said she has to go further. MP Neil Carmichael told The Independent he wanted to hear a clear statement at the despatch box from Brexit Secretary David Davis that Parliament would have a vote in all circumstances. He said that it should be made “without qualification”.
On Thursday in Brussels, Ms May caved in to pressure over the decision to increase NICs, saying the controversial measure would not come in until the autumn and signalled that it could be subject to mitigation, although she was still determined not to say she was backing down on it.
Tory MPs worried that the measure represented a clear breach of an election promise not to increase NICs had just spent 24 hours raising concerns in public.
One backbencher pushing for change said: “The Government will say it’s not a U-turn. And it won’t be a U-turn, that is, right up until the moment that it is a U-turn.”