LONDON (AFP) - New BBC director-general Tony Hall took up his post on Tuesday, starting the task of restoring the reputation of the world's biggest broadcaster that has been rocked by a child sex abuse scandal.

Lord Hall walked into the the BBC's Broadcasting House headquarters in central London to tackle an in-tray topped with the fallout from police investigations which concluded that the corporation's late presenter Jimmy Savile was one of Britain's most prolific sex offenders.

The British Broadcasting Corporation was subsequently damaged by a botched television report wrongly indicating that a lawmaker was a paedophile.

Engulfed by the scandals, Lord Hall's predecessor George Entwistle resigned as director-general in November after just 54 days in the job.

Lord Hall, 62, a former head of BBC news, returns to the corporation after more than a decade as chief executive of the Royal Opera House.

In an internal e-mail message to staff, he said the corporation was "learning the lessons" from recent "difficult times".

"We are now winning back trust, something which will always be the most precious commodity for our organisation.

"The BBC sets incredibly high standards. At our best we provide a service like no other.

"Our challenge is to perform at our best all of the time."