First Secretary of State Damian Green has said the country's circumstances would have been better had the electorate voted to remain in the European Union.
Mr Green – a long-term ally of Ms May who serves as her de facto deputy – was a prominent campaigner for Remain alongside the Prime Minister during the 2016 referendum.
When asked by journalist Emily Maitlis on the BBC's Newsnight whether it would have been better if the UK had opted to stay in the EU, he said "it would have been".
"I was on the board of the Stronger In campaign – nobody fought harder than me for Remain – so I don't resile from my views," he said.
He dismissed the question, calling it "silly", since "there's not going to be a another referendum today".
The Prime Minister refused to answer a similar question hours earlier.
When asked during an LBC interview whether she would vote differently if a poll was held again, she said: “I voted Remain for good reasons at the time but circumstances move on and I think the important thing now is that we should all be focused on delivering Brexit and delivering the best deal.
“You are asking me to say, 'How would I vote in a vote now', against a different background, a different international background, a different economic background.”
When pressured by presenter Iain Dale to give an answer she 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 came to a judgement and I'd do exactly the same this time round.
“But we are not having another referendum and that's absolutely crucial.”
Critics have seized on the comments, claiming they are evidence the Prime Minister still harbours pro-EU feelings.
Health Secretary Jeremy Hunt, who was another prominent Remain campaigner during the referendum, has since hardened his position on the EU and earlier this month described the EU Commission as "arrogant".
Talks between the EU and Britain remain at an impasse as the bloc is demanding key issues, including the Northern Ireland border, the rights of EU citizens and the contents of a divorce bill, are resolved to its satisfaction before trade talks begin.
The Prime Minister recently warned the public to prepare for a no-deal scenario in a letter to MPs that addressed contingency plans for businesses and tourists.
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