LONDON (AFP) - British Prime Minister Theresa May on Tuesday (Oct 10) refused to tell a radio station whether she would back European Union membership in another referendum, as she leads her country out of the bloc.

"I don't answer hypothetical questions," May told LBC radio station when asked how she would vote if a Brexit referendum were held now.

The prime minister said she had "good reasons" when she backed EU membership in the 2016 vote, when she was interior minister, but that circumstances have changed in the interim.

"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," said May.

"I'm 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're not having another referendum."

May vowed to push on with implementing Britain's historic departure from the bloc, despite being uncertain of whether she would back Brexit at the polls.

Her radio appearance comes as divorce talks continue this week at a sluggish pace in Brussels, while at home the prime minister attempts to reassert her authority after seeing off a plot to oust her.

Many colleagues within May's Conservative Party rallied around her after the attempt by a group of her MPs was exposed on Friday, in the wake of widespread reports of infighting within cabinet over Brexit.

She has also been weakened by a chaotic address to the party's annual conference last week, during which she fell into coughing fits, was interrupted by a prankster, and the set started to fall apart.

May's position has been called into question repeatedly since June, when her decision to call a snap election backfired with the Conservatives losing their parliamentary majority.