The Metropolitan Police launched an investigation into the 53-year-old in 2016 over allegations of serious sexual offences said to have involved a teenage boy under 16 between 1997 and 2000.
The investigation was closed in 2019 after prosecutors decided there was insufficient evidence to bring charges.
The BBC said it was aware of a police investigation into allegations against Mills of a historical sexual offence in 2017, but sacked him last month after new information was brought to the corporation’s attention.
In a statement last week, Mills said: “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 seven years ago, I hope the public and the media will understand and respect my wish not to make any further public comment.”