Veteran BBC broadcaster Paul Gambaccini says he has been through “12 months of trauma”, with news he won’t be charged over historic sexual assault allegations.

The 65-year-old, who has joint US and British citizenship, was arrested in October 2013 as part of the police investigation into sex abuse set up after the scandal over late BBC presenter and predatory paedophile Jimmy Savile.

Prosecutors said on Friday there was insufficient evidence to bring a case against Gambaccini.

The pop music expert was detained alongside another man, now aged 75, over offences alleged to have taken place over a two-year period in the early 1980s.

The allegations were made by two males who were aged between 14 and 15 at the time.

In a statement, the Crown Prosecution Service did not name either man being investigated and gave only their ages.

“We have concluded that the available evidence does not offer a realistic prospect of conviction for any of the alleged offences,” said Baljit Ubhey, the chief public prosecutor for London.

In a statement, Gambaccini said he had been “falsely accused”, adding he would not be speaking further about his year on bail.

“I will never trivialise the 12 months of trauma to which I have been unjustly subjected,” he said.

“I’ll be back at work soon.”

A BBC spokesman said the corporation would meet with him “to discuss the next steps shortly”.

Having earned a reputation as the “Professor of Pop” following his 1968 radio debut, the broadcaster went on to host classical music programs.

Gambaccini was a vocal figure after the Savile scandal erupted in 2012, saying it was known among BBC staff that the late presenter targeted vulnerable young people.

Savile was one of the BBC’s top stars for decades but it was revealed after his death in 2011 that he was a serial paedophile and sex offender.