But Mr Johnson insisted that a separate codicil setting out amendments to the backstop plan would not be “good enough”, indicating that he is holding out for changes to the text of the agreement itself.
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 designed to keep the Irish border open after the UK’s withdrawal.
Meanwhile, Prime Minister Theresa May has offered further talks with Labour in an attempt to secure cross-party consensus on Brexit.
In a letter to Jeremy Corbyn, she questioned his call for a customs union with Brussels, but offered concessions in other areas and said she wanted talks between Labour and Tory teams “as soon as possible”.
Mr Johnson accused Mr Corbyn of trying to “frustrate” Brexit by demanding a customs union, which he said would prevent the UK from striking its own trade deals.
“It’s clear that Jeremy Corbyn… he’s done a complete U-turn,” Mr Johnson told BBC Radio 4’s Today programme.
“He now wants to frustrate Brexit very largely by staying in a permanent customs union.”
On the Northern Ireland backstop, Mr Johnson said: “The argument is now about how to get out of the backstop. And how to make sure that the UK isn’t locked in that prison of the customs union.
“I think that you would need to have a time limit.”
Asked if changes to the backstop proposals could come in a separate codicil to the Withdrawal Agreement, Mr Johnson said: “I don’t think that would be good enough.”
Responding to the conditions for a Brexit deal set out by the Labour leader in a letter last week, Mrs May said she wanted the Tory and Labour teams to consider “alternative arrangements” to the Irish backstop.
She insisted her deal already met many of the conditions he had set.
The existing Political Declaration – the part of the Brexit deal setting out the goals for the future UK-EU relationship – “explicitly provides for the benefits of a customs union – no tariffs, fees, charges or quantitative restrictions across all sectors and no checks on rules of origin”, said the PM.
But she said it also recognises the development of the UK’s independent trade policy.
Mr Corbyn’s demand is for a customs union that gives the UK a say on future trade deals the EU might strike – something Brussels appears unlikely to accept.
The Prime Minister said: “I am not clear why you believe it would be preferable to seek a say in future EU trade deals rather than the ability to strike our own deals?”
She also questioned whether the call for completely “frictionless” trade would mean reneging on Labour’s commitment to end free movement by requiring single market membership.
The Prime Minister has previously ruled out a customs union, which would restrict the UK’s ability to strike trade deals, and could face Cabinet resignations if she changed her position.
Treasury Chief Secretary Liz Truss refused to rule out resigning if Mrs May backed a customs union.
She told Sky News: “I absolutely do not think that should be our policy.”
Mrs May rejected Labour’s demand to automatically follow EU rules on workers’ rights and environmental protection.
But she said the Government is prepared to commit to asking Parliament if it wishes to follow suit if standards change.
She told Mr Corbyn: “It is good to see that we agree that the UK should leave the European Union with a deal and that the urgent task at hand is to find a deal that honours our commitments to the people of Northern Ireland, can command support in Parliament and can be negotiated with the EU – not to seek an election or second referendum.”
Mr Corbyn has repeatedly said there should be an election if Mrs May cannot get a deal through Parliament and he has faced concerted pressure from some in his party to push for a second public vote.
There appears little prospect of an imminent breakthrough with Brussels, and Mrs May might not bring her deal back for a decisive vote this month.
Labour will use a vote expected on Thursday to attempt to force the Prime Minister to bring the deal back for a showdown by February 26 to prevent her “running down the clock” before Brexit.
But the Prime Minister is expected to offer MPs a further chance to vote on non-binding amendments which could influence her Brexit strategy on February 27.
The move is aimed at postponing a rebellion by ministers who are committed to removing the possibility of the UK crashing out of the EU without a deal on March 29.