Theresa May faces calls to grant free votes on alternatives to her Brexit strategy after MPs dramatically seized control of the process.

The Prime Minister’s fragile authority suffered another blow as three ministers quit to back a Commons amendment enabling MPs to take control of Commons business to stage a series of “indicative votes” on alternatives to her deal.

But Eurosceptics signalled they could now swing reluctantly behind Mrs May’s deal, with influential backbencher Jacob Rees-Mogg saying “the choice seems to be Mrs May’s deal or no Brexit”.

“I have always thought that no deal is better than Mrs May’s deal, but Mrs May’s deal is better than not leaving at all,” the European Research Group chairman said on a ConservativeHome podcast.

He added that Brexit may now be a “process rather than an event” and it could take time to fully break away from Brussels.

The three ministers who quit were among 30 Conservative MPs to defy the whips and support the cross-party amendment which was passed by 329 to 302 – a majority of 27 – in another humiliating reverse for Mrs May.

The defeat heaps further pressure on Mrs May’s position and could increase the chances of an early general election if MPs back plans for a softer Brexit which would be unacceptable to the Prime Minister or Tory Eurosceptics.

The Prime Minister will address Tory MPs at a meeting of the 1922 Committee on Wednesday amid speculation that setting a timetable for her departure could sway more Conservatives to back the deal.

Article 50 extension: key dates
(PA Graphics)

At Tuesday’s regular Cabinet meeting, the Prime Minister is expected to be confronted with calls for free votes on the rival options.

“Many around the Cabinet table will argue for a free vote so Parliament can truly show what it would support,” a Cabinet source said.

Alistair Burt, who quit his Foreign Office role in order to vote for the Commons amendment, said: “Parliament should seek urgently to resolve the situation by considering alternatives freely, without the instruction of party whips, and Government should adopt any feasible outcome as its own in order to progress matters.

“I did not believe the Government was prepared to do that, so had to vote to ensure this happens.”

Steve Brine, who quit as a health minister, suggested the revolt in favour of the indicative votes amendment could actually boost the chances of Mrs May’s deal finally getting through by persuading Tory Eurosceptics such as Mr Rees-Mogg it was the best form of Brexit on offer.

House of Commons Brexit vote: Oliver Letwin amendment
(PA Graphics)

“Those on my side who don’t like the deal, maybe they will realise that the House of Commons is prepared to act,” he told the BBC.

“And, anything from here, as far as they are concerned, gets softer in terms of Brexit.”

He added: “You have to accept that a second referendum or revoking Article 50 are on the table because they will probably be some options.”

The 2017 Tory manifesto ruled out membership of the single market and customs union and Mrs May told MPs on Monday that “no one would want to support an option that contradicted the manifesto on which they stood for election to this House”.

But Mr Brine said: “You also have to remember that the manifesto of 2017 did not win a majority in the House of Commons.”

Richard Harrington, who resigned as a business minister, said the Government was “playing roulette” with people’s lives and livelihoods in its handling of  Brexit.

The plan for MPs to take control of the Commons agenda was led by Tory former minister Sir Oliver Letwin and Labour’s Hilary Benn, chairman of the Brexit Select Committee.

Mr Benn told BBC Radio 4’s Today programme: “If the Government isn’t going to do its job then Parliament is going to have to take responsibility, and that is what we are doing on Wednesday.”

He suggested that Wednesday would see MPs vote on a piece of paper for as many of the options as they liked.

There would then be a similar process on Monday in an effort to whittle down the number of options under consideration.

The Government warned the move had set a “dangerous, unpredictable precedent” for the constitution and it was essential that any options put forward by MPs were actually “deliverable”.

Theresa May
Theresa May leaves the House of Commons following the key Brexit votes (Dominic Lipinski/PA)

The Prime Minister warned she would not feel bound by the results of any indicative votes.

“No Government could give a blank cheque to commit to an outcome without knowing what it is,” she said.

But Labour leader Jeremy Corbyn said the Government must “take this process seriously”.

The vote came after the Prime Minister acknowledged that she still did not have sufficient support to bring back her deal to the Commons for a third “meaningful vote”.

She said she would continue her efforts to build support for the deal – defeated by 230 votes in January and 149 votes in March – and stage a vote before the end of the week.

The European Council last week set a deadline of Friday for her to secure parliamentary approval for her Withdrawal Agreement if the UK is to leave the EU with a deal on May 22.

If she cannot get it through the Commons, then the UK has until April 12 to propose a different approach or crash out of the EU without a deal.

Her admission came shortly after a phone call with DUP leader Arlene Foster, who made clear the Northern Irish party was not giving up its opposition.