In an exclusive interview with the Press Association, the Commons Leader insisted she would stay in the Cabinet to help Mrs May deliver Brexit and denied that the PM was softening her stance over a customs union in a letter to Mr Corbyn.
British Secretary of State for International Trade Liam Fox, Swiss Federal Councillor Guy Parmelin and Liechtenstein's Foreign Minister Aurelia Frick shake hands after signing a trade agreement in Bern, Switzerland. The Prime Minister's official spokesman said she would address MPs a day earlier than expected to give MPs more time to "digest the content" ahead of a series of votes scheduled for Thursday, allowing parliamentarians another chance to alter the course of Brexit or seek a delay.
That might mean that she's back before the end of this month with something concrete to vote on.
Brexit minister Stephen Barclay will meet European Union negotiator Michel Barnier on Monday ahead of a crunch moment in parliament on Thursday, when lawmakers will try to force May to change course or give up control of the exit process.
Mr Johnson accused Mr Corbyn of trying to "frustrate" Brexit by demanding a customs union, which he said would prevent the United Kingdom from striking its own trade deals.
In their letter to Mrs May, the group describing themselves as "patriotic, pragmatic Conservatives" said it the United Kingdom is "not ready to leave" on the scheduled date of 29 March.
It also follows an exchange of letters between Mrs May and Labour leader Jeremy Corbyn.
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"We would have to be able to get out by a certain time and we would have to be able to get out of our own volition".
If London and Brussels manage to reach a deal for an orderly Brexit, the bilateral agreements between Switzerland and the European Union will continue to apply to Britain until the end of the transition period, the statement said.
'Non-EU members do not have a say in EU trade policy so to pretend that you could do so is a unsafe delusion, ' he said.
He added: "I am concerned that with 46 days to go the Prime Minister is simply running down the clock, mindful that the next EU Summit is March 21 and if she's is trying to run the clock down Parliament has to step in with a hard stop to say we are not going to accept that".
Mrs May said securing frictionless trade for goods was "one of our key negotiating objectives".
The Leave campaign figurehead was speaking as Brexit Secretary Stephen Barclay prepared for talks with European Union chief negotiator Michel Barnier as the Government stepped up efforts to secure changes to the backstop, which is created to keep the Irish border open after the UK's withdrawal.
"I don't think that would be good enough", he said.
She said the government needed to "get serious" about policy on a customs union and guarantee to "legislate for the protections around workers' rights".