LONDON - MPs are set to vote on a second referendum amendment for the first time as well as on a cross-party proposal that would allow the Commons to take control of the Brexit process from the beleaguered Theresa May.

The Speaker unexpectedly selected a second referendum amendment from Sarah Wollaston for voting on Thursday night. Wollaston, who recently defected from the Conservatives to the Independent Group (TIG), has won support from the Lib Dems for her amendment. It says the UK’s exit from the EU should be delayed for the purpose of legislating for and conducting a public vote in which staying in the bloc is an option on the ballot paper.

But it creates a dilemma for Labour’s leadership. The party has said it would support a second referendum amendment to “stop a damaging Tory Brexit”, but there are at least two dozen Labour backbenchers hostile to the idea.

Early indications were that the Labour front bench would abstain so killing it off for Thursday, according to several of the party’s MPs, who argued it was too soon to put the issue to the Commons.

One MP said: “This looks like pure political posturing by TIG – instead of focusing on the key issue today which is securing an extension which could actually deliver a People’s vote.”

Alastair Campbell, a leading figure in the People’s Vote campaign, agreed. The former Labour spin doctor said it was “wrong to press a People’s Vote extension today when the issue is [article 50] extension”.

Arguing that a second referendum was “a possible solution to the current crisis, not an option within it”, Campbell added there would be more opportunities ahead when other options to solve the Brexit crisis had been exhausted.

Caroline Flint, a Labour MP opposed to a second referendum, said she was “really delighted” that Bercow had selected the amendment because she would have the opportunity to vote against it. “I urge the House to oppose a second referendum,” Flint added.

The amendment with the best chance of passing is the backbenchers’ proposal submitted by Labour’s Hilary Benn and supported by his fellow Labour MP Yvette Cooper plus seven others including the Conservatives Oliver Letwin and Dominic Grieve.

The amendment says it is designed “to enable the House of Commons to find a way forward that can command majority support” by effectively allowing MPs to wrest control of parliamentary time from May’s government.

The debate on Wednesday would allow the Commons to decide whether to hold a series of indicative votes to find which Brexit approach could command a majority in the house. It is also supported by SNP, Liberal Democrat and Plaid Cymru MPs.

The amendments are two of four amendments taken by the Speaker for Thursday evening’s vote on extending article 50. Voting is expected to start at about 5pm.

But there were complaints in the Commons after Bercow refused to select another amendment, opposing a second referendum, which had attracted the support of 111 MPs, mostly hard-Brexit Tories, with the support of the DUP and a handful Labour MPs. It called on MPs to declare that “the result of the 2016 EU referendum should be respected and that a second EU referendum would be divisive and expensive and therefore should not take place”.

Signatories of the amendment in the name of the Conservative MP Lee Rowley included Boris Johnson and Bill Cash plus the DUP’s Nigel Dodds and Labour MPs including Gareth Snell, Caroline Flint, Denis Skinner, Kate Hoey and John Mann.

A Labour frontbench amendment, chosen by the Bercow, instructs May to seek an unspecified extension to article 50 to avoid exiting the EU on 29 March without a deal and “to provide parliamentary time for this house to find a majority for a different approach.”.

That would imply a long extension as few believe that a radically different Brexit deal to the one already negotiated by May can be agreed quickly with the EU. The fourth and final amendment selected by Bercow came from Chris Bryant, a Labour backbencher. Bryant wants MPs to vote on whether they believe that Theresa May can put an unchanged Brexit deal before the Commons to a vote.

Parliamentary precedent holds that the government cannot ask MPs to vote twice on the same issue during the same session of parliament, to prevent the executive bullying the Commons by putting the same measure to a vote repeatedly.

The main other second referendum amendment came from the SNP, which called for an extension to article 50 in time to hold a second referendum. It added that “Scotland must not be taken out of the European Union against its will”. But it was not selected for debate.