Theresa May’s deal is “doomed” and Brexit should be delayed in order to secure a better agreement, former defence secretary Michael Fallon has said.

Fallon, who had been one of the prime minister’s closest allies, issued the warning as the PM headed for Wales and Northern Ireland to try to sell the deal she brought back from Brussels on Sunday.

Speaking to BBC Radio 4′s Today programme on Tuesday morning, Fallon said: “My fear is that this deal gives us the worst of all worlds – no guarantee of smooth trade in the future and no ability to reduce the tariffs that we need to conclude trade deals with the rest of the world.

“So, unless the House of Commons can be persuaded somehow that those are possible, then I think, yes, the deal is doomed.”

Fallon added: “If it’s possible to get a better deal, to send the negotiators back to Brussels for two or three months, to postpone the actual leaving date for two or three months, I still think that in the long term that would be in the best interest of the country.”

MPs are due to vote on the government’s deal on December 11 – and all signs point to the prime minister losing.

Tory backbenchers are furious at the agreement which they worry will keep the UK indefinitely tied to the EU without the ability to strike independent trade deals. 

May has already survived an attempted coup by hardline Brexiteers who tried to oust her ahead of the EU rubber-stamping the deal.

David Lidington, the de facto deputy prime minister, dismissed Fallon’s attack.

“There is no point in sending negotiators back, when negotiators on the other side are making clear that this is the deal on the table, this is the choice,” he said.

In an attempt to rally support fo her deal, May has challenged Jeremy Corbyn to a Brexit TV debate, and has launched an intensive two-week campaign to try to get her EU exit agreement through the Commons.

May told The Sun on Tuesday: “I am going to be explaining why I think this deal is the right deal for the UK – and, yes, I am ready to debate it with Jeremy Corbyn, because I have got a plan. He hasn’t got a plan.

“Exactly how it might be done, if he takes it up, would be a matter for the broadcasters to determine.

“I am willing to stand up and explain why I think it is the best possible deal available for the UK.”

The comments came after Donald Trump appeared to undermine May’s Brexit deal, telling reporters: “Sounds like a great deal for the EU.”

In response, a Downing Street spokesman said: “The political declaration we have agreed with the EU is very clear we will have an independent trade policy so that the UK can sign trade deals with countries around the world – including with the US.

“We have already been laying the groundwork for an ambitious agreement with the US through our joint working groups, which have met five times so far.

“The US Trade Representative also issued a call for views from the public on a future UK-US free trade agreement earlier this month.”