Boris Johnson has admitted he cannot remember the lunch at which he is alleged to have groped a female journalist – despite repeatedly denying the incident took place.

Asked again about the explosive claim made by award-winning journalist Charlotte Edwardes, which has rocked the Conservative conference, the prime minister said: “I can tell you that it is not true.”

But, asked if he could recollect the lunch 20 years ago, he acknowledged: “I don’t to be honest, I have no memory whatever.”

The admission risks undermining Mr Johnson’s attempts to slam a lid on the controversy, which has placed fresh focus on his personal behaviour.

In the interview, with ITV News, he was immediately asked: “If you don’t remember it, how are you so sure it’s not true?”

The interviewer demanded: “You don’t remember it prime minister, so why should we take your word over somebody who does?”

Mr Johnson attempted to switch the conversation to “our domestic agenda”, insisting: “There are more announcements at this conference than I have seen anywhere.”

Ms Edwardes wrote a weekend article recounting a lunch at The Spectator magazine in 1999 where she said Mr Johnson, the-then editor, squeezed her thigh.

Mary Wakefield, the wife of Downing Street adviser Dominic Cummings, has denied she was a second woman that Ms Edwardes alleged was also groped by their boss at the lunch.

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Cabinet ministers have swung behind the prime minister, arguing his denial should be believed, but one former Conservative MP said the accusations raised questions about Mr Johnson’s character.

In the interview, the prime minister again made the controversial claim that the “stuff being thrown at me” was motivated by a desire to block Brexit.

“This is a very turbulent time in British politics and people will want to try and knock the government off course because, at the moment, the task is a difficult mission, but a vital mission, that is to get Brexit done by 31 October,” he said.

In a separate interview with Sky News, Mr Johnson was asked about alleged favours granted to his friend Jennifer Arcuri while he was London mayor – appearing to deny, for the first time, that they had an affair.

The interviewer said the debate was over possible misuse of public funds, continuing: “That’s why I’m asking if you were having a sexual relationship.”

The prime minister replied: “I can certainly say there was absolutely no question of that at all.” He has previously refused to answer questions about his private life.