Jeremy Vine and Piers Morgan are among the high-profile figures who have called for the unnamed presenter at the heart of the BBC scandal to come forward publicly for the good of his colleagues at the corporation.
Fresh claims about the anonymous man emerged yesterday, following previous allegations over payments he had made for sexually explicit photos.
The Sun newspaper's front page today also reported that a 23-year-old person has claimed the presenter broke lockdown rules to meet them during the pandemic in February 2021.
Mr Vine is one of several celebrities, including Nicky Campbell, Gary Lineker and Rylan Clark, who have publicly stated that they are not the presenter in question, since the allegations were first made public.
Speaking on his Channel 5 show, Mr Vine - who also hosts an afternoon show on BBC Radio 2 - said: "It's his decision but he needs to come forward now, I think.
"I know his survival instinct has kicked in and I know he saw what happened to Phillip Schofield, but my God look at the damage to the BBC, look at the damage to his friends, to those falsely accused - and the longer he leaves it the worse it will be for him."
Mr Vine said he thought "very carefully" before posting his tweet last night urging the unnamed presenter to reveal himself, adding: "I know the individual concerned. I am very worried about his state of mind and what this is doing to him.
"I haven't spoken to him but I gather from somebody who has that he is described as angry and keen to play it long.
"Now to me that means that he wants to be anonymous for as long as possible hoping that he can one day walk back into the building."
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Posting online yesterday, Mr Vine said the latest allegations would result in "yet more vitriol being thrown at perfectly innocent colleagues" at the BBC.
"I'm starting to think the BBC Presenter involved in the scandal should now come forward publicly," Vine wrote on Twitter.
"These new allegations will result in yet more vitriol being thrown at perfectly innocent colleagues of his.
"And the BBC, which I'm sure he loves, is on its knees with this. But it is his decision and his alone."
However, former Blue Peter presenter Richard Bacon, who was sacked from the programme in 1998 for taking cocaine, hit back at Mr Vine's tweet.
"Stop it. You're more emotionally intelligent than this," he said.
"We don’t know the complexities of what his family are going through. Or what dark thoughts are running through his head.
"Irrespective of what he’s done wrong. You can walk off people wrongly guessing it’s you for 5 minutes."
Talk TV host Piers Morgan said the unnamed presenter should come forward "for the good of his colleagues, the BBC and himself".
"It's only a matter of time before he loses agency in the situation (and) somebody blurts out in parliament, or on a less responsible network," he said.
"For the good of his colleagues, the BBC, and himself and his reputation, it is surely time for that presenter to reveal his own identity, and to vow to clear his name and defend himself if that's what he can do."
David Keighley, former BBC news producer and director of News-watch, said the presenter's continuing anonymity was causing "reputational damage" to the man's colleagues.
"What needs to be done here is a very thorough investigation, and conclusions can't be jumped to until we know the full facts," he said, speaking to Times Radio.
"But at the same time, you've got a developing situation, which is because it has been contained in the way it has. And we stress again, we don't know precisely why that is.
"It is causing reputational damage, not just to the BBC itself, but to other presenters. It's spreading like a cancer, is the problem."
Publicist and strategist Mark Borkowski also told Times Radio the presenter could not go unnamed much longer.
"We've got a situation where it's an ongoing car crash and the BBC is so glacial about how they're dealing with this, because this is a 21st century problem," he said.
"They're dealing with 20th century, sort of communication processes. We're above it all.
"There's a heavy legal duty on this and a duty of care, which makes it a nightmare for anybody managing this and to say that, okay, but I don't believe that it can carry on for much longer that this person is not named".
BBC director-general Tim Davie has ordered a review to "assess how some complaints are red flagged up the organisation".
He has said the BBC is dealing with a "complex and difficult situation" after the "serious allegations".
