Theresa May has refused to say she would back Brexit if the referendum on quitting the European Union was held now.

In a move likely to anger Tory Brexiteers, the Prime Minister, who backed Remain, repeatedly sidestepped questions over which camp she would be in.

During an appearance on LBC, Mrs May insisted she was being “open and honest” when she could not give an answer.

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Theresa May's handling of Brexit: approval rating(PA Graphic)

Asked if she had changed her mind about how to vote, she replied: “I don’t answer hypothetical questions.

“I voted Remain for good reasons at the time but circumstances move on.”

Mrs May was told Health Secretary Jeremy Hunt had switched from Remain to Leave because former Chancellor George Osborne’s gloomy economic predictions had failed to materialise.

Presenter Iain Dale said: “If he says he can change his mind I don’t quite understand why you can’t seeing as you are Prime Minister leading us into Brexit.”

“Yes and I’m Prime Minister ensuring I’m going to deliver Brexit for the British people,” she replied.

Pressed again, Mrs May said: “I could say I would still vote Remain or I would vote Leave just to give you an answer to that question.

“I am being open and honest with you. What I did last time round was I looked at everything and I came to a judgment and I would do exactly the same this time round.

“But we are not having another referendum and that’s absolutely crucial.”

Liberal Democrat deputy leader Jo Swinson said: “It is staggering that even the Prime Minister isn’t convinced by the Government’s approach to Brexit.

“If Theresa May doesn’t have any faith in her own Government’s policies, why is she still driving this country towards the cliff edge?

“Theresa May says she would weigh up the evidence again, she shouldn’t deny that right to the British people.

“The public must have the chance to change their mind if they want to, once the Government comes back with a deal.”

Mrs May’s de facto deputy Damian Green suggested he would stick to his Remain vote from last year’s referendum but described the question put to the PM and him as “meaningless”.

Damian GreenDamian Green (David Cheskin/PA)

The First Secretary of State told Channel 4 News: “Well, I was on the board of the Stronger In campaign so my views on Europe are well known and I don’t resile from anything I said during the election campaign.

“Of course, the fact is it’s a meaningless question because there’s not going to be a referendum tomorrow, so it’s a purely hypothetical question.”