David Cameron and Ken Clarke have joined a concerted push by Conservative heavyweights for Theresa May to accept her hard Brexit policy is doomed.

The former prime minister urged his successor to “consult more widely” with other parties on the exit talks, saying: “I think there will be pressure for a softer Brexit.”

The call was quickly followed by a plea from Mr Clarke, the former Chancellor, for new trade barriers “between us and our most important market in the world” to be avoided at all costs.

Meanwhile, Philip Hammond, the current Chancellor, is believed to be leading a Cabinet push for the Prime Minister to abandon her plan to pull out of the EU’s customs union.

Yesterday, Sir John Major warned Ms May that her stance was “increasingly unsustainable”, with the loss of her Commons majority, insisting: “A hard Brexit was not endorsed by the electorate.”

However, Ms May – at least publicly – is refusing to change course. The Cabinet endorsed the current Brexit policy when it met yesterday.

And speaking in Paris, alongside French president Emmanuel Macron, she claimed: “The timetable for the Brexit negotiations remains on course and will begin next week.”

Shortly before, the Prime Minister appointed Steve Baker, the leader of Parliament's most prominent Eurosceptic group, to a key ministerial post in the Brexit department.

Mr Cameron’s intervention came when he spoke to a conference in Poland, where he warned the dramatic election results made Ms May’s approach “difficult”.

Arguing the Parliament “deserves a say” on any deal, he said: “Perhaps [there is] an opportunity to consult more widely with the other parties on how best we can achieve it.”

Mr Clarke, speaking to BBC Radio 4, called for a new Brexit policy “in the national interest, which can command a majority on a cross-party basis”.

Warning of revolts to come, he said Ms May would be making a big mistake if she simply sought the agreement of the Democratic Unionist Party and then expected “the entire Conservative party to agree”.

It was most crucial to achieve “no new customs barriers, no new regulatory barriers, no tariffs put in place”, hampering trade with the EU.

Laying bare the Parliamentary turmoil ahead, he said: “There has to be a majority for something – but nobody knows quite what it is.”

However, Mr Clarke said Mr Macron was “wrong” when he suggested Britain could still reverse Brexit. “We are destined now to leave the European Union,” he insisted.

The Times newspaper reported that Mr Hammond will lead a battle within the Government to keep Britain inside the customs union – even though it would prevent trade deals being struck with non-EU countries.

One source described the Treasury as being in “street-fighting mode”, with support likely to come from Damian Green, the Prime Minister's newly appointed deputy.

Leaving the customs union would impose tariffs on British exporters, plus the huge red tape of filling in forms and putting goods through customs checks.