The prime minister ruled out answering any “hypothetical questions” when quizzed by Sky News on her support for Brexit during a trip to South Africa.
Asked whether she would now vote to leave the EU, the former Remain supporter said: “We’re not in the business of having a second referendum on Brexit.
“What we’re in the business of doing is delivering Brexit.
“So actually what somebody would vote for today is not the issue.
“The issue is: are we doing what the British people wanted? The answer is yes – this government is delivering it.”
Mrs May also refused to be drawn on a warning from her former foreign secretary, Boris Johnson, that her Chequers proposal would risk harming Britain’s economy.
She said simply that the proposed plan for a future relationship with Brussels would be a “a good deal for the UK” and “a good deal for the EU”.
And Mrs May paid tribute to her “great welcome” to South Africa, after the prime minister joined in with a group of dancing pupils during a visit to a school in Cape Town.
“I think the chances of Strictly Come Dancing coming calling are pretty minimal,” she said.
“I have to say it was a great welcome from the school today, everybody was dancing, it was great excitement, a fantastic moment and a great welcome to South Africa.”
Responding to a question about nicknames it may have earned her, Mrs May said: “I’ve been called many things in my time.”
Tom Brake, a Liberal Democrat MP and supporter of the People’s Vote campaign for a referendum on the final Brexit deal, told Sky News “we cannot allow Theresa May to avoid this crucial question”.
He asked: “Why is she pursuing a policy that she knows will make our country poorer and weaker? That is not what anyone, including her, voted for in 2016.”
Jeremy Corbyn also recently refused six times to say whether he thought Britain would be better off after Brexit.
The Labour leader has not ruled out backing another referendum but previously said it is not something he is “calling” or “asking” for, and claimed “the ship has sailed” on Britain staying in the EU.