Brexit is scheduled for March 29 and British Prime Minister Theresa May has not been able to finalise an arrangement with the bloc after her deal was rejected by the British Parliament with overwhelming majority in January.
However she questioned his support for a customs union with the EU, saying it would prevent Britain from striking free trade deals with other countries around the world.
British worldwide trade secretary Liam Fox and Swiss Economy Minister Guy Parmelin signed the bilateral trade agreement in Bern on Monday.
She said it was possible to pass bills "quite quickly" with "goodwill" from the Commons and Lords, but added: "It's just not possible to say how quickly it could be done, but obviously it depends on the way in which there is adequate debate on the meaningful vote and that's what the Prime Minister is determined to do".
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.
"Should the United Kingdom leave the European Union on 29 March without a deal, the agreement will come into effect on a provisional basis from 30 March 2019", the government statement said. 'I don't think there is any mileage in trying to do a deal with Labour, ' he told the BBC.
Mrs May sparked the furore by penning a letter to Mr Corbyn (pictured inset bottom) saying his call for the United Kingdom to stay in a customs union would hamper free trade deals - but stopped short of ruling it out.
"The idea that you can have a customs union with the EU and at the same time, as an outside country, have an effect on EU trade policy, is to not understand the EU treaties".
"We shouldn't be put in a position where the clock is run down and the prime minister says it's either my deal or even worse".
But James Brokenshire, the communities secretary, promised MPs would be allowed another chance to vote on what they wanted to happen next if no new deal had been presented to them by February 27.
The agreement should remove the uncertainty a "hard" Brexit scenario posed for some 15,000 citizens of the three non-EU nations who live in Britain.
Mrs May maintains it would not give Britain an independent trade policy, but Mr Corbyn says it is the best way to protect jobs.
The Prime Minister said: "I am not clear why you believe it would be preferable to seek a say in future European Union trade deals rather than the ability to strike our own deals?"
Mrs May said securing frictionless trade for goods was "one of our key negotiating objectives". I think you would need to have a time limit.
Mrs May is to give a statement to Parliament on Tuesday, a day earlier than planned.
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.