Cabinet members have warned a new election is nearing as Theresa May lost grip on the Brexit process during another fraught night in the House of Commons.

A series of top ministers raised the prospect of a third UK election in four years after MPs voted – by 329 votes to 302 – to take control of parliamentary process away from the prime minister so that they can set out how they think Britain should escape its political crisis.

The loss saw three Remain-minded junior ministers quit their jobs so they could join forces with a cross-party drive that is now likely to push the government towards a longer delay to Britain’s departure and a much softer Brexit.

In a sign of the stand-off to come, Ms May gave a strong indication she will not pursue a course that flies in the face of the 2016 Brexit vote or 2017 election result, like a new referendum, an arrangement excluding a free trade policy or one allowing the continuation of free movement.

She conceded however that she will not yet bring the twice-defeated deal she struck with the EU back for a third vote, as there is currently insufficient support to pass it.

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One cabinet minister told The Independent that the “chicken endgame of Brexit” had now begun, with eurosceptic MPs who previously refused to back Ms May’s deal will soon be forced to decide if they can accept a potentially terminal delay to Britain’s departure from the bloc instead.

In dramatic scenes, MPs backed the plan tabled by ex-Tory minister Sir Oliver Letwin, which now allows backbenchers to start the process of organising a series of “indicative votes”, in a bid to discover what Brexit compromise carries a majority in the Commons.

While the votes pencilled in for Wednesday will be non-binding on the government, Sir Oliver, who was backed by fellow ex-Conservative minister Nick Boles and Labour’s Hilary Benn, has suggested the group could use its new power to try and pass actual legislation leaving the government no choice but to follow parliament’s will.

Ministers who quit to oppose the government included Richard Harrington, Steve Brine and Alastair Burt.

In his resignation letter, Mr Harrington said: “At this critical moment in our country’s history, I regret that the government’s approach to Brexit is playing roulette with the lives and livelihoods of the vast majority of people in this country who are employed by or otherwise depend on businesses for their livelihood.

“Further, as the UK’s industry minister, the clear message I have been receiving from the business community is that the failure to secure a deal and to rule out a hard Brexit is resulting in cancelled investment decisions, business being placed abroad, and a sense of ridicule for British business, across the world.”

As the prospect of the defeat loomed, Ms May made clear that she could not simply abide by whatever MPs demanded, saying: “No government could give a blank cheque to commit to an outcome without knowing what it is.

“So I cannot commit to delivering the outcome of any votes held by this house. But I do commit to engaging constructively with this process.”

Earlier in the day during an emergency cabinet meeting, Brexit secretary Stephen Barclay repeated a warning that the government could be left with no option but to call an election if parliament demands an outcome the government is unwilling to deliver.

Attorney general Geoffrey Cox agreed at the cabinet table that if MPs mandate a softer Brexit an election might be inevitable, with Andrea Leadsom said to have concurred.

One minister said: “There was a discussion, it was not about setting a direction of travel, more just a statement of fact that things might become ungovernable.”

During a statement in the Commons, Ms May also confirmed that the date of Brexit has now changed in international law to 12 April and would also be altered in UK statute in the coming days.

Theresa May says as things stand "there is not sufficient support" to ask MPs to vote on her Brexit deal for a third time

A member of the cabinet told The Independent: “All the focus is now on 12 April. Parliament will do what it will, and it will be down to Conservative MPs who have refused to back the deal to now do so if they don’t want to see Brexit delayed for a long time.

“This is now the chicken endgame of Brexit. It’s coming to an end in the coming days.”

Brexit secretary Stephen Barclay had urged MPs to vote down the Letwin amendment earlier in the debate, saying: “It’s the prime minister’s deal that is the way to deliver what the people voted for in 2016 and 2017.