Esther McVey has refused to give her full support to Theresa May’s Brexit strategy amid growing unrest among Conservative backbenchers over her EU exit plan.

The work and pensions secretary told a think tank event in London that the prime minister would “deliver the Brexit that Britain voted for” but the pro-Brexit minister stopped short of giving her public backing to Ms May’s new blueprint.

The prime minister managed to unite her cabinet behind the Chequers compromise but the peace was shattered when Boris Johnson and David Davis both dramatically resigned in protest.

Ms May faced taunts from MPs that her plan was “dead in the water” after she narrowly avoided Commons defeats by making a series of concessions to ardent Brexiteers over customs rules.

Former foreign secretary, Mr Johnson, piled on the pressure by using a Commons resignation statement on Wednesday to urge the prime minister to abandon her “miserable” version of Brexit.

Meanwhile, Ms McVey, when asked if she had confidence in the PM’s Chequers plan, said: “I will say that I have full confidence in the prime minister to deliver the Brexit that Britain voted for.”

In a letter to voters in his Shipley constituency, obtained by The Yorkshire Post, he said: “Politics is all about trust and once it is lost it is impossible to win back.

People's Vote march – demanding vote on final Brexit deal Show all 30 1 /30 People's Vote march – demanding vote on final Brexit deal People's Vote march – demanding vote on final Brexit deal Mandatory Credit: Photo by Guy Bell/REX (9725259aq) Marching down Whitehall - People's March for a People's Vote on the final Brexit deal. Timed to coincide with the second anniversary of the 2016 referendum it is organised by anti Brexit, pro EU campaigners. People's March for a People's Vote, London, UK - 23 Jun 2018 Guy Bell/REX Rex People's Vote march – demanding vote on final Brexit deal Demonstrators carry banners and flags as they participate in the People's March demanding a People's Vote on the final Brexit deal, in central London on June 23, 2018, the second anniversary of the 2016 referendum. Tens of thousands of people demonstrated in London on Saturday calling for a second vote on Britain's departure from the European Union. / AFP PHOTO / Niklas HALLE'NNIKLAS HALLE'N/AFP/Getty Images NIKLAS HALLE'N AFP/Getty Images People's Vote march – demanding vote on final Brexit deal A young protestor shouts as she takes part in the People's Vote demonstration against Brexit Getty Images People's Vote march – demanding vote on final Brexit deal A woman holds a placard as she joins EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participating in the 'People's Vote' march in central London, Britain June 23, 2018. REUTERS/Henry Nicholls HENRY NICHOLLS Reuters People's Vote march – demanding vote on final Brexit deal epa06833888 Pro-EU demonstrators take part in a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal A protester's pro-EU t-shirt EPA People's Vote march – demanding vote on final Brexit deal epa06833892 A pro-EU demonstrator waves a European Flag during a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Demonstrators carry banners and flags as they participate in the People's March demanding a People's Vote on the final Brexit deal, in central London on June 23, 2018, the second anniversary of the 2016 referendum. 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Tens of thousands of people demonstrated in London on Saturday calling for a second vote on Britain's departure from the European Union. / AFP PHOTO / Niklas HALLE'NNIKLAS HALLE'N/AFP/Getty Images NIKLAS HALLE'N AFP/Getty People's Vote march – demanding vote on final Brexit deal epa06833964 A young pro-EU demonstrator takes part in a People's March anti-Brexit rally in Parliament Square in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Gina Miller and Caroline Lucas EPA People's Vote march – demanding vote on final Brexit deal epa06834044 Tens of thousands of people march through London during a People's March anti-Brexit demonstration, in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal epa06833264 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Tens of thousands of people march through London EPA People's Vote march – demanding vote on final Brexit deal epa06833265 Thousands of people march through London during a People's March anti Brexit demonstration in London, Britain, 23 June 2018. Protesters are calling for a referendum on the final deal. The protest is taking place on the second anniversary of the Brexit referendum. EPA/ANDY RAIN ANDY RAIN EPA People's Vote march – demanding vote on final Brexit deal Demonstrators at the People's Vote March Getty People's Vote march – demanding vote on final Brexit deal 'Two months too young to decide on my future' REUTERS People's Vote march – demanding vote on final Brexit deal Crowds taking part in the People's Vote march for a second EU referendum at Trafalgar Square in central London. PRESS ASSOCIATION Photo. Picture date: Saturday June 23, 2018. See PA story POLITICS Brexit. 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PRESS ASSOCIATION Photo. Picture date: Saturday June 23, 2018. See PA story POLITICS Brexit. Photo credit should read: John Stillwell/PA Wire John Stillwell PA People's Vote march – demanding vote on final Brexit deal Crowds gather on Pall Mall PA People's Vote march – demanding vote on final Brexit deal A man resembling Britain's Foreign Secretary Boris Johnson, joins EU supporters Reuters People's Vote march – demanding vote on final Brexit deal EU supporters, calling on the government to give Britons a vote on the final Brexit deal, participate in the 'People's Vote' march in central London, Britain June 23, 2018. 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“Many people have told me that as a result of this they have lost trust in the PM to properly and fully deliver the referendum result.

“It is with much sadness that I have to say that I have also lost trust in her to deliver the referendum result too.”

Mr Davies said that Tories faced losing power to Jeremy Corbyn’s Labour if they failed to deliver the Brexit the country voted for in the 2016 EU referendum.

“Failure to keep our promise to the electorate will almost certainly lead to the catastrophe of Jeremy Corbyn becoming prime minister and I cannot sit back and allow that to happen,” he wrote.

“This has not been an easy decision and I have agonised over it, but I know in my heart of hearts it is the right decision.”

The Brexiteer is the third MP to go public with his letter to Graham Brady, the chair of the 1922 committee of Tory backbenchers, although the total number is unknown.

Mr Brady must receive 48 letters from MPs – equivalent to 15 per cent of the parliamentary party – to trigger a no confidence vote in the prime minister.

Andrew Bridgen and former junior minister Andrea Jenkyns have also publicly announced that they have submitted letters to Mr Brady.

However, Eurosceptic MP Simon Clarke declared on Wednesday that he had withdrawn his own letter, after changing his mind about wanting to topple the prime minister.