The leading Brexiter, who dramatically quit the cabinet last week in protest over the withdrawal agreement negotiated by the prime minister, said he did not advocate staying in the EU but that May’s plan was an inferior option.

Asked on BBC Radio 4’s Today programme what he would do if he had to choose between May’s deal or no Brexit at all, Raab said: “Well, I don’t have to choose that. I’m sorry, I’m not going to give way to hypothetical scenarios. I’ll keep fighting for the best, most successful Brexit.”

Pressed further on whether he thought the deal would be worse than staying in the EU, he replied: “Well, I’m not going to advocate staying in the EU but if you just presented me terms, this deal or EU membership – we’d effectively be bound by the same rules without a control or voice over them – yes, I think this would be even worse than that.”

Asked about reports cabinet ministers were considering a negotiated no deal, asking the EU to give the country another year of transition and paying some money in return, Raab said: “I would certainly be up for making a best final offer and then considering no-deal deals like that but I think, in fairness, that’s not the course the prime minister has taken. I respect all of my cabinet colleagues, from those that campaigned remain to leave, and those in between.

“But the reality is the deal we’ve got on the table is … I think inevitably we will see parliament vote this deal down and then I think some of those other alternatives will need to come into play.”

Raab resigned last Thursday, a day after tense cabinet talks over May’s EU exit strategy, saying he could not “in good conscience” support the deal agreed by the cabinet. He singled out in his resignation letter the proposed arrangement to avoid a hard border with Ireland through a backstop arrangement, calling it a “very real threat to the integrity of the United Kingdom”.

He added: “I cannot support an indefinite backstop arrangement where the EU holds a veto over our ability to exit.” He also said the deal amounted to a “hybrid of the EU customs union and single market obligations”.

But defending May’s “bespoke” withdrawal proposals, the education secretary, Damian Hinds, told the Today programme: “I think the British public do want us to get on with it and that’s what I hear repeatedly from constituents, but what we have now is actually a very compelling deal.

“This political declaration contains the instructions for negotiators for the next phase to basically deliver an economic relationship between the UK and the EU which will be stronger and closer than any other advanced economy has with the EU. That didn’t look possible a few months ago. We’ve come an awful long way since then and, as I say, this is a very strong proposition.”

May is set to attend a crunch summit of EU leaders on Sunday where it is hoped her deal will be endorsed.

Hinds, who backed remain during the referendum, added: “This is a political commitment and we’re going to have 27 nations coming together on Sunday to consider it and to commit to it and it is basically about how that future relationship is going to be shaped. It’s the legal position with the EU, that they can only negotiate with a country when it’s not a member so we’ll be negotiating on that after we’ve left.

“But the framework is there. Actually, there’s quite a lot of detail, more detail and more ambition than many people were expecting and it does mean that we’ll have that very close economic relationship with it but still being able to strike our own trade deals around the world. That is explicit in the text, and also making sure we deliver firmly on the instruction from the British people in the referendum on things like ending free movement. We can move to a skills-based immigration system, out of the common agricultural policy, out of the common fisheries policy but in a way which is good for our economy and good for people’s jobs.”

Asked about reports of cabinet colleagues discussing an alternative no-deal strategy, he replied: “There are no leavers and remainers. From the moment the referendum was over we all have a duty to deliver on the clear instruction that we got from the British people.”

He also warned: “There’s a risk on the one hand, beyond that, of no Brexit at all. There are people who are trying to thwart Brexit, and there’s also a risk of no deal. Neither of those two things are attractive and that is why this deal, which is a strong deal, I believe will gain more and more traction.”

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