Theresa May has been warned that "dozens" of Tory MPs are prepared to vote to delay Brexit unless she takes the prospect of a no-deal scenario off the table.

In a major challenge to the prime minister, a group of normally loyal Leave and Remain-backing Conservatives have called for a free vote on a backbench bid from Tory grandee Oliver Letwin to prevent the UK crashing out of the EU without a deal next month.

Tory MPs Andrew Percy and Simon Hart, who lead the Brexit Delivery Group, have written to chief whip Julian Smith to say that many MPs are deeply troubled at the prospect of no deal.

It comes as it emerged that fresh Brexit talks have been scheduled for early next week as Ms May heads towards another Commons showdown on her EU withdrawal stance.

Mr Percy told the Today programme: "We are a loosely aligned group and we have been very consistent as a group in support of the prime minister's deal but in that scenario dozens of my colleagues have made clear to us that they would want to vote in a way that would prevent a hard no-deal Brexit.

"A lot of colleagues are becoming very frustrated, a lot of colleagues have compromised from their positions.

"We are a group who have brought together both Leavers and Remainers, people who are seeing the intransigence from some of our other colleagues – people who are perhaps in denial of the parliamentary arithmetic actually is on some of these matters – and people are frustrated that we are prepared to make compromises and others are not."

The letter to the chief whip, published in the Daily Telegraph, said: "The reputation for competence of both the party and the government depends on our ability to deliver an orderly exit, in line with the existing timescale.

Which MPs defected to form Change UK? Show all 12 1 /12 Which MPs defected to form Change UK? Which MPs defected to form Change UK? Change UK Details on the individual MPs are in the following photos Reuters Which MPs defected to form Change UK? Heidi Allen Anti-Brexit MP for South Cambridgeshire resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Chuka Umunna MP for Streatham since 2010 and prominent People's Vote supporter PA Which MPs defected to form Change UK? Anna Soubry The prominent anti-Brexit MP for Broxtowe resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Luciana Berger MP for Liverpool Wavertree since 2010, resigned from the Labour Party over bullying and anti-semitism PA Which MPs defected to form Change UK? Sarah Wollaston Anti-Brexit MP for Totnes resigned from the Conservative party on February 20 PA Which MPs defected to form Change UK? Joan Ryan MP for Enfield North resigned from the Labour party on February 19 citing its tolerance of a "culture of anti-Jewish racism" PA Which MPs defected to form Change UK? Ann Coffey MP for Stockport since 1992 Chris McAndrew / UK Parliament Which MPs defected to form Change UK? Gavin Shuker MP for Luton South since 2010 Getty Which MPs defected to form Change UK? Chris Leslie MP for Nottingham East since 2010 PA Which MPs defected to form Change UK? Mike Gapes MP for Ilford South since 1992 PA Which MPs defected to form Change UK? Angela Smith MP for Penistone and Stocksbridge since 2010

"Whilst we fully expect some changes to the backstop arrangements to be made by ministers in Brussels this week, there remains a chance that these will not satisfy some colleagues. Numerous members of our group have alerted us to their intention (should rejection of the deal look likely) to get behind amendments that are planned in the name of Oliver Letwin and others and which will have the twin effect of taking no deal off the table and delaying Brexit."

But former Tory leader Lord Howard rejected the calls for a delay to Brexit and insisted fears about a no-deal departure from the EU had been exaggerated.

"Parliament delegated the decision on whether we should leave the EU to the electorate at large," he said. "People voted in unprecedented numbers, by a clear majority, to leave. We must leave, and I believe we must leave on March 29."

He said he hoped there could be a deal but "if we can't then I think that actually the fears of a no deal have been exaggerated".

Support free-thinking journalism and attend Independent events

Meanwhile, Brexit secretary Stephen Barclay and attorney general Geoffrey Cox have announced they will hold further talks with EU chief negotiator Michel Barnier in the coming days over the divisive Irish backstop.

Ahead of crunch commons votes expected next Wednesday, Ms May will travel to an EU-Arab summit in Egypt this Sunday.

While government sources have been keen to dampen talk of a "deal in the desert", the PM is expected to have meetings with EU leaders on the sidelines of the gathering.