Ben Bradley and Maria Caulfield warned that the Prime Minister’s plans for close links with Europe after Brexit risked handing Jeremy Corbyn the keys to 10 Downing Street.
It comes after the resignations of Foreign Secretary Boris Johnson and Brexit Secretary David Davis over the proposals.
In her resignation letter, Ms Caulfield warned that the PM’s policy “may assuage vested interests, but the voters will find out and their representatives will be found out”.
“This policy will be bad for our country and bad for the party,” she added. “The direct consequences of that will be Prime Minister Corbyn.”
Mr Bradley said that the Brexit plan agreed at Chequers would damage the UK’s opportunities to develop global trade and be “an outward-looking nation in control of our own destiny” following Brexit.
“Being tied to EU regulations and the EU tying our hands when seeking to make new trade agreements will be the worst of all worlds,” wrote the MP, whose Mansfield constituency voted considerably in favour of leave.
“If we do not deliver Brexit in spirit as well as in name, then we are handing Jeremy Corbyn the keys to Number 10.”
Conservative chairman Brandon Lewis said: “Maria Caulfield and Ben Bradley have worked hard since the start of the year to promote women and young people on behalf of the Conservative Party.
“I wish them both well as they return to the backbenches to serve their constituents.”
Jeremy Hunt has been appointed new foreign secretary and Dominic Raab Secretary of State for Leaving the EU after the resignations of Mr Johnson and Mr Davis.
Amid a reshuffle of Theresa May’s top team, Culture Secretary Matt Hancock replaces Mr Hunt as health secretary and Attorney General Jeremy Wright becomes Culture Secretary. Geoffrey Cox has been appointed as Attorney General.