Former presenter Scott Mills has said that he has been subject to "rumour and speculation" since the BBC announced his sacking earlier this week.
In his first public statement since the news broke, the former Radio 2 breakfast host said that he "co-operated fully" with an investigation by police in London into allegations of an historic sexual offence.
In a statement released through his legal team, Mr Mills said: "The recent announcement that I am no longer contracted to the BBC has led to the publication of rumour and speculation.
"In response to this the Metropolitan Police has made a statement, which I confirm relates to me.
"An allegation was made against me in 2016 of a historic sexual offence which was the subject of a police investigation in which I fully cooperated and responded to in 2018.
"As the police have stated, a file of evidence was submitted to the Crown Prosecution Service, which determined that the evidential threshold had not been met to bring charges.
"Since the investigation related to an allegation that dates back nearly 30 years and the police investigation was closed 7 years ago, I hope that the public and the media will understand and respect my wish not to make any further public comment on this matter.
"I wish to thank from the bottom of my heart all those who have reached out to me with kindness, my former colleagues, and my beloved listeners, who I greatly miss."
BBC knew about 2017 police investigation into Scott Mills
Earlier, the BBC confirmed that it knew about the police investigation into Mr Mills in 2017, but said it "acted decisively" after receiving "new information" in the weeks prior to his sacking.
It terminated the presenter's contracts on Friday, days after taking him off air.
The Metropolitan Police launched an investigation into the 53-year-old in 2016 over allegations of serious sexual offences involving a teenage boy under 16 between 1997 and 2000.
He was questioned under caution by officers in July 2018. The Sun reported that Mr Mills denied the claims at the time and informed the BBC.
The newspaper said that bosses decided not to take the then-Radio 1 presenter off air and the case was dropped in May 2019 because of lack of evidence.
Hampshire Police said the sexual offences allegations were first reported by a third party in 2016 and the force logged the details and passed on information to the Metropolitan Police for investigation.
A BBC spokesperson said: "Scott Mills had a long career across the BBC, he was hugely popular and we know the news this week has come as a shock and surprise to many.
"We also recognise there's been much speculation in the media and online since Monday.
"We hope people understand that there is a limit to what we can say because we have to be mindful of the rights of those involved.
"What we can confirm is that in recent weeks, we obtained new information relating to Scott and we spoke directly with him.
"As a result, the BBC acted decisively in line with our culture and values and terminated his contracts on Friday 27 March.
"The BBC has made a significant commitment to improve its culture, processes and standards.
"Last year, following an independent culture review, we set out the behavioural expectations for everyone who works with or for the BBC and we were clear action would be taken if these were not met."
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Scott Mills sacked from BBC Radio 2 over 'personal conduct' allegations
Police closed sex offence investigation into Scott Mills due to lack of evidence
The BBC also apologised for not following up a separate allegation of "inappropriate communications" by Mr Mills raised by a journalist last year.
It has also been announced that a children's cancer charity has decided to "part ways" with the DJ, who had been a patron since 2021.
A statement from Neuroblastoma UK said: "Following his dismissal from the BBC, Neuroblastoma UK have taken the decision to part ways with Scott Mills and he is no longer a patron of our charity".
