Theresa May has been warned of fresh Tory revolt over her Brexit approach, as she faces a race against time to agree a deal with Brussels.

Despite winning plaudits for her upbeat conference speech, the prime minister’s reprieve was short-lived, as a senior Brexiteer told her to avoid a “political accident” by rethinking her Chequers plan just hours after she appealed for unity.

Time is running out for Ms May to break the deadlock with Brussels ahead of the European Council summit on October 17, which the EU has described as the “moment of truth” for a Brexit deal.

The prime minister is reportedly beginning a frantic diplomatic push with European leaders, after telling Tory activists in Birmingham that they risked ending up with “no Brexit at all” if they could not unite.

However Steve Baker, the former Brexit minister who resigned in protest over the Chequers plan, said even if only half the 80 Conservative MPs who oppose the plan voted against it, it would be enough to defeat the government.

He said Ms May would face a “substantial” revolt unless she changed course, and repeated his claims that 80 Tory MPs were prepared to vote for an amendment protesting against Chequers, which they believe keeps the UK too closely tied to the EU.

While he acknowledged that supporting a protest motion was a different matter to voting down an actual deal, he said the government whips would still struggle to get it through the House.

“We don’t want to have this accident. We are trying very hard to avoid these circumstances arising,” he told ITV’s Peston.

“Voting against a Chequers-based deal would be quite a high bar, I am not going to deny that. But what I am saying is that even if the whips did fantastically well and got the numbers down to 40 it still seems to me that it will be voted down.

“I am trying very hard to avoid that by being very plain with everybody on the record what I expect to happen if a Chequers-based deal comes back.”

Ms May sought to strike an upbeat tone in her speech to the Conservatives annual conference in Birmingham, where she promised an end to a decade of austerity.

She also insisted her Chequers plan was the only proposal that would honour the referendum result while avoiding the return of a hard border in Ireland.

But in a sign of her continuing woes, cabinet minister Andrea Leadsom refused to say whether Ms May should continue as prime minister after Brexit.

Ms Leadsom, who stood against the prime minister for the Tory leadership in 2016, praised Ms May for her performance but said “politics is a short-term game”.

Pressed on the matter, she said: “That’s all for the future. She has shown her absolute determination to fulfil the referendum.

“I just think politics is a short-term game, a week changes a lot.”

Ms Leadsom, a prominent Leave campaigner, said the Chequers plan met her “red lines” for Brexit, adding “that is the only deal that is on the table”.

She told the same programme: “It is also the only deal that keeps the United Kingdom together, that avoids hard infrastructure on at border between Northern Ireland and Ireland or – even worse – a border down the Irish Sea.”

Ms May emerged largely unscathed from the annual conference, despite pressure from hardline Brexiteers such as Boris Johnson and Jacob Rees-Mogg.

The next 10 days could be among the toughest of her premiership, as she will have to find a way to unite her DUP allies, different Brexit factions and the EU behind a deal.

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