Conservative MPs will be offered free votes if the Commons succeeds in seizing control of the Brexit process to find a “plan B”, a government minister has suggested.

Kwasi Kwarteng said it would be “surprising” if Theresa May decided to whip Tory MPs against alternative options likely to be debated next Wednesday.

Free votes – as demanded by pro-EU cabinet ministers – would dramatically increase the chances of MPs backing a softer Brexit, or even a fresh referendum.

Many ministers are believed to favour staying in the customs union or single market – while others are ready to back a Final Say public vote, supporters believe.

Answering an emergency question in the Commons, Mr Kwarteng, a junior Brexit minister, twice said he expected free votes – something refused by the prime minister so far.

It came as he was lambasted by MPs for refusing to say when the promised third “meaningful vote” on Ms May’s deal would take place – or even if it definitely would.

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Mr Kwarteng was asked if Tories would be released from the whip so the public could “truly see that we are acting in a way to try to find the best way forward”, if the deal is defeated again.

“Obviously, if the house is being asked to find a way forward, it would be surprising if those votes were not free votes,” he replied.

Amid surprise, the minister repeated: “I was referring to the indicative votes that were suggested by my right honourable friend [Tory MP Vicky Ford] in her question.”

He said the decision was “a matter for the business managers and will be taken as and when the debate will take place”.

In reality, it is a crucial decision for the prime minister – amid growing pressure for free votes, given the near certainty of defeat for the deal and the danger of a crash-out no-deal Brexit as early as 12 April.

Senior Tories descended into open warfare over the issue, as David Lidington, Ms May’s de facto deputy, met with opposition leaders to discuss how to facilitate the indicative votes.

The Independent was told that Mr Lidington was willing to engage in advanced discussions about how they should be carried out, including whether to use preferential ballots to find a clear winner.

But Steve Baker, the deputy leader of the hard Brexit European Research Group, said: “National humiliation is imminent through these indicative votes. The wrong Conservatives have the levers of power.”

The issue will come to a head on Monday, when a cross-party group of backbenchers attempts to commandeer the Commons business for Wednesday, to trigger a series of indicative votes on the best way forward.

The Monday amendment is expected to succeed, after losing by only two votes last week, given the escalating threat of a no-deal Brexit.

One suggestion is for MPs to tick boxes on a piece of paper listing the various Brexit options, perhaps allowing them to show support for more than one, before a winner is announced.

Despite Mr Kwarteng’s evasions, it is understood that No 10 is gearing up to bring the vote back on Tuesday, or possibly Wednesday.