Conservative lawmaker Phillip Lee, who resigned from the justice ministry in June over the government's handling of Brexit, told a packed pro-EU event on the sidelines of the party's annual conference that the ministers had told him so in private conversations.
With six months to go until Britain is due to leave the European Union, May is yet to reach an exit deal with the bloc, and both Labour and many lawmakers in her own party are threatening to vote against any deal in parliament.
"But we are continuing to focus on getting a good deal for the United Kingdom".
"At the heart of the Chequers plan is a free trade deal, a free trade area and frictionless trade. Crucially, I believe in delivering Brexit in a way that respects the vote and delivers on the vote of the British people while also protecting our union, protecting jobs and ensuring we make a success of Brexit for the future".
May has shown little sign of shifting away from her Chequers plan, named after her country residence where she hashed out an agreement on Brexit with her ministers in July, despite growing criticism that her proposals offer the worst of all worlds.
A number of influential MPs and supporters are expected to use the event in Birmingham to voice their concern over Mrs May's ability to see through the Brexit process, which could hand further impetus to Jeremy Corbyn after the Labour conference unfolded relatively incident free.
He added: "A no-deal Brexit is a proposal so damaging to our future that it can not be accepted".
She added: "What drives me, what drives the government, is the national interest".
"There are plenty of prominent people in British politics who want to stop Brexit in its tracks", she warned.
"Where they have problems, let's actually hear them and it's only then that you can actually identify what the issue really is, where there are issues that lie behind this".
Her remarks were an apparent riposte to Mr Johnson's implication, in an interview with the Sunday Times, that she was not fully committed to Brexit. But her response was sharp.
Manuel Valls, son "au revoir chaleureux" aux Français
Philippe à Valls: "La pire des choses lorsqu'on a eu l'honneur de diriger un gouvernement, c'est de susciter l'indifférence". A la fin de son discours, des députés LREM lui avaient réservé une standing-ovation pour lui rendre hommage.