In a statement, 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.”
The breakfast show host was abruptly taken off air by the BBC last week, before his sacking over allegations related to his “personal conduct” was announced on Monday.
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The 53-year-old last hosted his show on Tuesday, March 24 and signed off with: “See you tomorrow.”
He was questioned by police under caution in July 2018.
Mills was not charged with a criminal offence, and the case was closed due to a lack of evidence.
The Metropolitan Police does not identify people who are subject to an investigation before any charges are brought.
What was the Met Police statement?
A spokesperson said: “In December 2016, the Met began an investigation following a referral from another police force.
“The investigation related to allegations of serious sexual offences against a teenage boy. These were reported to have taken place between 1997 and 2000.
“As part of these inquiries, a man who was in his 40s at the time of the interview was questioned by police under caution in July 2018.
“A full file of evidence was submitted to the Crown Prosecution Service, who determined the evidential threshold had not been met to bring charges. Following this advice, the investigation was closed in May 2019.”
