Boris Johnson’s senior ministers have attempted to minimise the allegations that he groped a journalist’s inner thigh at a dinner in 1999 as the party tried to get its conference back on to the subject of Brexit and domestic policy.

Nicky Morgan, the culture secretary and former minister for women, gave her wholehearted backing to the prime minister, saying: there is “no truth in these allegations”, while housing minister, Esther McVey, suggested journalists needed to go back and check it really happened.

Another cabinet minister told the Guardian that the idea of Johnson “pinching a knee” was not inconsistent with what people already thought about him, given the history of affairs in his private life.

Play Video 0:46 Boris Johnson denies groping allegation – video

With the conference in Manchester overshadowed by the allegations, Downing Street advisers were talking up the prospect of a Brexit deal breakthrough, suggesting new proposals could be tabled within days. Allies claim the furore about the prime minister’s alleged sexual misdemeanours is “priced in” and will barely register with voters.

But Johnson continued to be pursued by the claims of groping, forcing him to give his first on-the-record denial that in 1999 he squeezed the leg of Charlotte Edwardes, now a columnist at the Sunday Times but then a junior journalist.

Asked whether he did it, Johnson said: “No, and I think what the public want to hear is about what we are doing to level up and unite the country.”

Pressed again on whether he was saying Edwardes had made it up, Johnson said: “I’m just saying what I’ve said. What the public want to hear is what we are doing for them and for the country and the investment in ways of uniting the country.”

Edwardes made the allegation in a column at the weekend, saying the woman on Johnson’s other side had also said her thigh was squeezed in a similar manner.

Cabinet ministers rallied round Johnson after Matt Hancock, the health secretary, said on Sunday that he would “entirely trust” Edwardes.

The Conservative party chairman, James Cleverly, told the BBC that if No 10 was denying the incident took place then “then I believe that”. He later told a fringe event that civil unrest “could happen” if Brexit was not delivered.

Play Video 0:26 Sajid Javid backs Boris Johnson over groping allegations – video

Sajid Javid, the chancellor, also gave his full backing to Johnson. “The prime minister has said that this is completely untrue and I have full faith in the prime minister. I don’t doubt what he has said for a second but I’m not going to get drawn into these allegations,” he said.

Boris Johnson groping a woman’s thigh? I can believe that | Suzanne Moore Read more

However, Toby Young, a former colleague of Johnson during his time at the Spectator, later told at an event at the conference that “people complained if Boris didn’t put his hand on their knee during lunch”.

Rumours swirled at the conference in Manchester about the identity of the second woman. Mary Wakefield, a commissioning editor at the Spectator and the wife of Johnson’s senior adviser Dominic Cummings, denied she was the person in question. “I am not the woman referred to in Charlotte Edwardes’s column. Boris was a good boss and nothing like this ever happened to me. Nor has Charlotte, who I like and admire, ever discussed the incident with me,” she said.

The furore overshadowed the second day of Conservative conference, as Johnson’s team attempted to turn the debate back to getting Brexit done, with advisers privately saying they still hope to achieve a deal with the EU.

Johnson is expected to table fresh Brexit proposals within days and Downing Street advisers insist that their first preference remains exiting the EU with a deal on 31 October, which would avoid having to comply with the requirements of the Benn deal forbidding a no-deal departure.

Even those cabinet ministers who privately express concerns about the prime minister’s strident tone in Brexit debates believe his clear messaging may help to force a deal through parliament.