The UK prime minister Theresa May was facing intense pressure to quit from within her own party on Sunday as she fought to keep her Brexit plan alive.

Eleven Cabinet ministers told the Sunday Times that they wanted her to be replaced, with some saying her departure could be key to securing backing for her Brexit proposals that have twice been rejected by parliament.

None of the ministers were named or have come out openly against the prime minister with one former party leader telling the plotters to “shut up” in the crucial final days before the UK leaves the European Union.

There was little indication that Mrs May planned to resign and two of her mooted successors said they wanted her to stay on. A leadership challenge by hard-line backers of Brexit failed in December last year and she could not be challenged under party rules for another year.

But some senior party members reportedly wanted her to fall on her sword. “The end is nigh,” an unidentified cabinet minister told the newspaper. “She won’t be prime minister in ten days’ time.”

Her deputy, David Lidington, was seen as the most likely to take over, according to reports. Mr Lidington, who has a low public profile, was seen as a potential unifying but short-term holder of the past.

But he told reporters on Sunday that he had no desire to take over the job and that working closely with Mrs May “cures you completely of any lingering shred of ambition” to do the job.

Environment Secretary Michael Gove, another named as a possible successor, said it was "not the time to change the captain of the ship".

Mrs May’s chancellor, Philip Hammond, also denied claims that he wanted Mr Lidington to take the top job. He told Sky News that changing the leadership would not help Britain through the political crisis.

"To be talking about changing the players on the board frankly is self-indulgent at this time," he told Sky News.

The volume of discontent against Mrs May’s leadership has risen after she was forced to request a delay from the European Union from the original March 29 date after failing to get enough parliamentary support for her plans.

European leaders told her that a delay would only be until May 22 and relied on Mrs May getting her much-criticised deal through, which has already been defeated by heavy margins by MPs, or coming up with a radical new plan.

She was meeting key pro-Brexit colleagues on Sunday at her country residence, Chequers along with ministerial colleagues including Mr Lidington.

Her critics who joined the discussions included former foreign secretary, Boris Johnson, and two former Brexit secretaries who all quit over her strategy.

The "lengthy talks" saw a range of issues discussed including whether there was enough support in parliament to have a third vote on her proposals this week, a Downing street spokesman said.

If Mrs May fails to get her own preferred option through parliament in the coming days, Britain could leave the European Union without a deal on future political and economic relations, which would be “catastrophically bad”, said Mr Hammond.

The alternative would be for Mrs May to return to the EU to request a longer delay, which would mean that the UK has to hold elections to the European parliament. Mrs May has previously ruled out such a scenario.

The behind-the-scenes leadership manoeuvring comes with few signs of majority agreement among MPs about the way to move forward. They are expected to hold a series of votes this week to try to come up with a plan.

A million people took to the streets of London on Saturday to protest against Brexit and call for a second referendum that could reverse the decision to leave the world’s largest trading bloc. A petition calling on the Government to cancel Brexit has also secured more than five million signatures.

Iain Duncan Smith – a former leader of the Mrs May’s Conservative Party – told the BBC that a leadership change could create complete chaos.

He said there would be “real disgust at the behaviour” of Cabinet ministers. “They should be apologising and they should shut up for God's sake,” he said.