Prime Minister Theresa May has to resign or the conservatives should force her to follow the party's massive local election losses, Iain Duncan Smith said.
The former Tory leader called Ms. May a & # 39; caretaker PM & # 39; and described attempts to find a deal with Labor as & # 39; absurd & # 39 ;.
It comes after the party suffered its worst local election result since 1995.
Other senior conservatives have called on Tory MPs to compromise with Labor to ensure that the Brexit is delivered.
But Mr. Duncan Smith, a leading Brexiteer in the party, said that many conservatives would refuse to support it.
He said Mrs. May should announce her departure "very soon" in the aftermath of the party's heavy losses.
If she did not go, the Committee of Deprived MPs of 1922 would force her to, he said.
The committee recently decided to change the party rules to allow for a new vote of confidence that could dispel Mrs. May.
However, some high conservatives believe that the vote in the 1922 Executive Committee changed after the Council's defeats.
Elections were held on Thursday for 248 English councils, six mayors and all 11 councils in Northern Ireland – where counting continues. There were no elections in Scotland or Wales.
Labor failed to achieve the expected profit in the elections, instead of losing 82 seats, while the Liberal Democrats benefited from the losses of Tory and received 703 seats. The greens and independents also made a profit.
Both Ms May and Labor leader Jeremy Corbyn have insisted that they continue to seek agreements between parties to leave the EU in accordance with local election results.
Mrs. May said it was clear that the public wanted "to see the Brexit problem resolved".
Health Secretary Matt Hancock said the party had to listen to the results and "was in the mood for a compromise."
Today, Mr. Hancock told the BBC Radio 4 program that the nation wanted MPs to "get out, deliver Brexit, and then move on."
& # 39; Difficult first steps & # 39;
Scottish Tory leader Ruth Davidson reiterated Mr. Hancock thinking about the & # 39; almighty kick & # 39; of the Conservatives and Workers Party in the local elections.
"The solution is not in the trenches of one extreme or the other – of overthrowing the referendum, or crashing without an appointment," said Mrs. Davidson, who spoke at the Scottish Conservatives conference in Aberdeen.
"It's in those colleagues who are currently sitting around the table and taking the difficult first steps towards each other.
"So I say to our party's negotiation teams and the Labor Party, who are currently locked up in talks – get Brexit sorted, a deal over the line and let Britain go."
The UK would leave the EU on March 29, but the deadline was reduced to October 31 after Parliament failed to reach an agreement.
Today, Hancock told the BBC Radio 4 program: the nation wanted MPs to "get out, deliver Brexit, and then move on."
Mr. Hancock said that the Tories should evolve into Labor's proposal of a permanent customs union – to resolve the impasse in Westminster.
Being part of the EU customs union means that once goods have left customs in one country and the commonly agreed rates (import duties) have been paid, they can be moved to other countries in the union without further costs.
A country does not have to be a member of the EU to be part of the customs union, but members cannot negotiate their own independent trade agreements with countries from the rest of the world.
Mrs May's government has previously ruled out that she will remain in a customs union after the UK has left the EU because it would prevent the UK from pursuing its own trade policy.
Labor said that the EU may show flexibility with regard to the problem and that the UK can "participate" in future trade agreements.
Mr Hancock suggested "to think of something in between" and called for "an open dialogue in which we can conclude an agreement".
& # 39; Find a solution & # 39;
Foreign Minister Jeremy Hunt said there was a "glimmer of hope" that a compromise could be reached between the "core voters" of the conservatives and the working class.
"If we can find a solution that delivers the benefits of the Customs Union without adapting to current arrangements, then I think there will be potential," he said.
He added that although he supported the withdrawal agreement reached between the EU and Ms. May, things might be done to make it "more acceptable" for Labor without compromising the "things we think are essential ".
But he also warned that a customs union would not be a "long-term solution".
And environment minister Michael Gove called on MPs to support Mrs May's deal – which Parliament rejected three times.
He said "democracy requires" MPs to vote for the deal, and he urged politicians from all parties "to unite to respect the outcome of the referendum"
& # 39; Sewn-on & # 39;
Secretary of Shadow Brexit, Sir Keir Starmer, said cabinet ministers currently attach more importance to the next conservative leadership competition than the Brexit.
In particular, the Labor advocate said that Mr Hunt's remarks provided "even more evidence" that many in the cabinet felt "the most important thing at the moment" was the race to be Mrs. May's successor.
Labor & # 39; s MP for Redcar Anna Turley also responded to Mr Hunt's comments that a customs union was not a long-term solution, tweeting: "This is why we cannot trust the Tories by making a deal that is choked in number 10 and that they are trying to unravel under their next leader."