Background:

Savile used to host a TV show called JIM'LL FIX IT, in which he'd "grant the wishes" of a number of viewers each week, usually kids.

A kid called Gareth Jenkins wished to be on DOCTOR WHO, so in 1985, DOCTOR WHO did a JIM'LL FIX IT crossover special, "A Fix with Sontarans". The special features the incumbent Doctor (Colin Baker), returning companion Tegan Jovanka (Janet Fielding), and Savile and Jenkins as themselves, facing regular villain species the Sontarans.

The plot of the episode is largely irrelevant. However, one thing about it is that Baker mentioned he disliked Savile and found working with him a thoroughly unenjoyable experience. This wasn't something Baker, who hadn't been privy to the allegations, came up with after they broke to look enlightened. In a featurette on the DVD release that included the episode — a release went on sale in 2006, several years before Savile's death and the subsequent headlines — he mentions he found Savile "non-inclusive," "self-congratulatory," and, somewhat less seriously, "much more frightening than the Sontarans".

This 100% comes through in the episode. There's one point at which Savile kisses Tegan's hand and the Doctor noticeably winces. Also, during the sequence with Savile at the end of the episode, as Savile is interacting with Jenkins, the Doctor draws closer to Jenkins, seemingly intending to protect him. Notwithstanding that Baker didn't know about the allegations, the overall effect very much makes it seem like the Doctor did — and, since the Doctor is a time traveller semi-permanently based in the vicinity of London, he probably would have.