British worldwide trade secretary Liam Fox and Swiss Economy Minister Guy Parmelin signed the bilateral trade agreement in Bern on Monday.
She has said she wants to bring a revised deal back to parliament for a vote "as soon as possible" but has not yet set a date for doing so.
"This new agreement lays the foundations for the two parties to continue their sound economic and trade relations once the United Kingdom has left the European Union", the Swiss government said in a statement (here in English). Foremost was a demand that May seek a "permanent and comprehensive UK-wide customs union".
Britain is due to leave the European Union on 29 March but has yet to find a deal which is acceptable to both Brussels and lawmakers at home, raising the prospect of a disorderly exit that could damage the world's fifth largest economy.
But May's office published her reply to Corbyn late on Sunday (10 February), showing little appetite for a U-turn which would risk splitting her fractious party by ruling out the scope for Britain to strike its own trade deals around the world.
May and her government have repeatedly said membership of a customs union would prevent it having an independent trade policy - something they have promoted as one of the main economic benefits of leaving the EU. During his speech, Mr Johnson said: "I don't think there is any mileage for Theresa May or the Government in trying to a do a deal with Labour".
"I found Corbyn's letter interesting in tone and in content", Barnier said earlier in the day in Luxembourg of the Labour leader's Brexit proposals, sent to May.More news: Teen defies anti-vaccine parents, gets shots
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Mr Corbyn has repeatedly said there should be an election if Mrs May can not get a deal through Parliament and he has faced concerted pressure from some in his party to push for a second public vote.
"Labour will just try to trap Theresa May. No point winning Labour MPs, by losing Tories!"
I think you would need to have a time limit. But the former foreign secretary insisted the mechanism would need to expire before the next general election in 2022.
The Prime Minister has spent the last week visiting Dublin and Brussels in an attempt to get changes on the controversial Irish backstop, and was expected to discuss her progress on Wednesday.
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 agree that the longer this goes on, the more risky it gets, obviously", Stewart said.
Mr Barnier's deputy Sabine Weyand made clear that the European Commission is not pinning its hopes on the United Kingdom eventually deciding to mount a second referendum, telling a conference in Germany that the only option was a structured exit.