The BBC has today opened an inquiry into its culture and practices at the time Jimmy Savile allegedly sexually abused young people.

The investigation, which is being led by former appeal court judge Dame Janet Smith and launches on the first anniversary of Savile’s death, will also establish if the BBC’s whistle-blowing policies are fit for purpose.

Former Sky News head Nick Pollard is already examining if the shelved Newsnight story on the Jim’ll Fix It star was mismanaged by senior staff at the corporation.

It comes after Lord Patten, the chair of the BBC Trust, said the corporation will hold nothing back in establishing the truth, “however terrible”.

In an article for the Mail on Sunday, headlined: “Can it really be that no one inside the smug BBC knew what that psychopath was doing?”, Patten said resolving the mounting “filth” had become his “immediate priority”.

The strongly-worded missive heaps pressure on director general George Entwistle to establish the facts as quickly and effectively as possible, or risk “squandering public trust”.

Patten added: “No grandstanding, no covering our backs. My primary task with my fellow trustees is to sort this out, as fast as we can, once and for all. Our public expects no less.”

Police are investigating claims that Savile sexually abused 300 young people over a 40-year period. As part of the inquiry, former pop star Gary Glitter was arrested and bailed on Sunday on suspicion of sex offences.

Savile’s family have also broken their silence for the first time since the scandal exploded. Savile’s nephew Roger Foster told BBC Radio 5 Live that they were disbelieving of the allegations when they first emerged.

“I was horrified when I saw the original programme. As the weeks have gone by, and the various allegations have come out, the number of allegations have been so great that I now believe that the vast majority of them are true,” Foster said.

“I am so absolutely devastated and disappointed that this dark side is the side that he will be remembered for. I’m also devastated and disappointed and very sympathetic towards the people who have kept this dark secret all of their lives.”