John Allan, the former Tesco chairman, is to see out the remainder of his term at Imperial College London weeks after he stepped back from the role amid unsubstantiated claims about his behaviour.

Sky News has learnt that Mr Allan was effectively reinstated as chair of the university’s council until the end of the year.

Mr Allan, who has had a successful 50-year business career running and serving as a director of some of Britain’s biggest companies, but was effectively forced to step down early as chair of Tesco and Barratt Developments in May amid the fallout from the crisis at the CBI, the business lobbying group.

He is himself a former CBI president.

Several women alleged that he had made inappropriate remarks or touched them, prompting him to deny that any of the incidents took place other than commenting to one woman that a dress had suited her figure.

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Mr Allan said he had not even been present at a number of the events at which his alleged misbehaviour was said to have taken place.

In a memo from Professor Hugh Brady, Imperial’s president, on Tuesday, Mr Allan was given a green light to resume his duties.

“Council was briefed on the search for its new chair of Council which is underway,” Prof Brady wrote.

“It agreed that John Allan should carry out his activities as chair until the end of his term on 31 December this year, after which he will step down.”

In a public statement on 22 May, Imperial had said that the allegations against Mr Allan had been discussed with him and at a Council meeting ten days earlier.

“At this Council meeting, it was noted that none of these allegations relate to his role at Imperial, no complaints had been received by Imperial and that John vigorously denies the allegations,” it said on 22 May.

“Nevertheless, John decided that in the broader best interests of the Imperial community, he would step back from his Imperial activities until the matter is resolved.

“Council, which is responsible for appointing its chair, will keep the matter under review.”

Mr Allan’s effective reinstatement may underline the unease felt in many quarters about his treatment by the boards on which he served.

Speaking to Sky News’ Sophy Ridge last month, he said he had been “propelled under the nearest bus”.

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“Now, having crawled out from two successive buses and still standing, I’m going to plan over the next few months to talk to a lot of people who know a lot more about this than me to sort of see if we can devise a better way so the next person who is subject to this sort of allegation is more fairly treated.”

Mr Allan has also stepped back from the mentoring partnership he had built with Anna Joseph, his colleague.

Earlier this month, Sky News revealed that Tesco had picked the Burberry chairman, Gerry Murphy, as his successor.

A spokesman for Mr Allan declined to comment.

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