Allegations that the Defence Secretary quit an earlier job after a junior colleague reported their fling to a manager are a “private matter”, Theresa May says.

However, the Prime Minister’s spokesman conceded that Gavin Williamson could yet be investigated if an official complaint was made about his comments about the relationship.

Mr Williamson has been in the spotlight since his extraordinary decision to reveal his “flirtatious relationship” with a married woman at Elgin & Hall, a fireplace manufacturer in North Yorkshire.

The key ally of Mrs May – tipped as a future prime minister – told the Daily Mail he decided to leave the company, on amicable terms, in order to save his marriage to Joanne, who forgave him.

But it has now been claimed that Mr Williamson departed after a meeting was held to discuss the problem with senior executives from parent company Aga Foodservice Group.

Asked if the Prime Minister was confident that her former chief whip was being truthful about the events, her spokesman replied: “This is a private matter which predates his time as an MP or a minister.”

However, the spokesman acknowledged that Mark Garnier had been investigated last year over buying sex toys for a staff member, even though that also happened before he became the trade minister.

“There was a complaint in relation to Mark Garnier. I’m not aware of anything in this instance,“ he added.

Asked, therefore, if Mr Williamson could be referred for investigation under the ministerial code if a complaint was made, the spokesman said: “I’m not getting into speculating.”

Asked, if the Prime Minister had “full confidence” in Mr Williamson, despite the conflicting accounts, he replied: “Yes.”

The Defence Secretary claimed the fling “never went further” than sharing a kiss with the woman “a couple of times” and that it “stopped as suddenly as it had started”.

However, he is under pressure to explain whether he was subject to an internal disciplinary process and why he kept the job at the firm off his official and social media profiles.

Meanwhile, Mr Williamson is also under fire after, in a separate interview on the same day, he warned Russia could cause “thousands and thousands and thousands” of deaths in a cyber-attack.

The Russian defence ministry ridiculed the claim and the Ministry of Defence was forced to deny that he had leaked military intelligence.

That interview appeared to spark a briefing war between allies of Mr Williamson and Boris Johnson, another leadership contender.