Responding to the SNP’s Westminster leader, Ian Blackford, during Prime Minister’s Questions, Ms May again refused to say she would vote for Britain to leave the EU.
Instead she answered: “There is no second referendum. The people of the United Kingdom voted and we will be leaving the European Union in March 2019.”
Mr Blackford claimed the Prime Minister, who backed the Remain campaign in last year’s referendum, “could not answer a simple question” and said she should “come off the fence”.
The exchange came hours after an LBC interview in which the Prime Minister refused three times to say if she would vote for Britain to leave the EU if another referendum were held.
She told host Iain Dale: “Well, I voted Remain for good reasons at the time, but circumstances move on.
"The important thing now is we should all be focused on delivering Brexit and delivering the best deal.
"But you're asking me to say how would I vote in a vote now against a different background, a different international background, a different economic background."
Mr Dale fired back: "So you can't tell me that you would vote Leave now?
"[Health Secretary] Jeremy Hunt, when I interviewed him at the conference, told he that he voted Remain in the referendum. He was a chief advocate of Remain [but] he said now he would vote for Brexit because he says George Osborne's economic predictions did not come true and he said he was fed up with the belligerent attitude of the European Commission.
"He says he could change his mind. I don't quite understand why you can't, seeing you are Prime Minister leading us into Brexit?"
A stuttering Ms May replied: "Iain, I could sit here and I could say I'd still vote Remain or I'd vote Leave just to give you an answer to that question.
"I'm being open and honest with you. What I did last time around was I looked at everything and came to a judgement and I'd do exactly the same this time around.
"But we're not having another referendum and that's absolutely crucial."
Ms May's deputy, Damian Green, took a clear stance, telling BBC Newsnight the UK "would have been" better off staying in the EU.
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