The BBC presenter Tony Livesey is to “step back” from his radio show after allegations were raised about his previous career as the editor-in-chief of David Sullivan’s Sport Newspapers.

The BBC said Livesey, 62, would be stepping away from presenting his late-night 5 Live show for “a short time” while the corporation considers the issues raised by a Panorama investigation, which accused Sullivan, a billionaire and co-owner of West Ham United, of sexually exploitative and predatory behaviour towards women over several decades.

Sullivan has denied the allegations, stating through his lawyers: “I categorically deny all of these complaints.”

The investigation also aired questions for Livesey, with one alleged victim stating that he had arranged a meeting between her and Sullivan.

Livesey told the Times he had “no recollection” of introducing the young woman to Sullivan and that it was “not part” of his job to do so. He said that he had had “practically zero” contact with anyone appearing in the paper, such as female models.

The BBC also pointed to a passage in Livesey’s 1998 book saying that he and Sullivan had devised the idea for the “countdown to 16” feature, which featured countdowns to models’ 16th birthdays, when they could be pictured topless legally for the first time.

Livesey has since said the feature was “categorically” not his idea and that large parts of his book were “fictionalised” to make it appear he was “at the centre of all stories”, even if he had not been.

A BBC spokesperson said: “The Panorama investigation included allegations about Tony Livesey which we take seriously. We also note Tony has firmly denied the allegations. He has asked to step back from presenting his radio show for a short period and we will be considering the matters raised by the programme. We will not be commenting further at this stage.”

Sullivan, 77, announced his resignation as a director and co-chair of West Ham United on Saturday, before a joint investigation by the BBC and the Times that reported on seven women who had accused him of sexual misconduct went public.

Three alleged Sullivan had abused his power as the owner of the Sport newspapers to prey on them for sex when they were seeking work. Four accused him of exploitative and predatory behaviour, including allegations he tried to pressure them into sex during business meetings.

Livesey became editor-in-chief at the Sport titles after starting as a reporter. He spent 18 years at the company. He left in 2006 to concentrate on his broadcasting career at the BBC.

Until Tuesday’s announcement, Livesey presented the 10pm to 1am show Monday to Thursday on 5 Live. He did not present the show on Monday night, the evening that the joint Panorama and Times investigation into Sullivan went public.

A stand-in host, Qasa Alom, started the show by interviewing the BBC investigative reporter behind the Panorama programme.

One woman alleged she had been taken to the offices of the Sport newspaper titles in Manchester, where she was introduced to Livesey, then the editor. She said he then called Sullivan to set up a meeting.

The same woman then described an unwanted sexual encounter with Sullivan, which took place during the meeting. She said she thought it had been a meeting about her career, but claims Sullivan told her she would have more prominent work if she had sex with him.

At the time he stepped down from the Sport, Livesey said: “It’s a much maligned newspaper in places, but those in the business know that no national newspaper could make a profit from day one to now without being excellent in its field.

“The Independent launched in the same year as us and it’s made a loss every year, as far as I’m aware. We’ve made a profit every year.

“When the big stories come along, we do them seriously, but we just try and give people a laugh, and that’s all I’ve done for 18 years.”