Well I don't know what did or didn't get to Starmer, and quite frankly I find it absurd to believe anything the state has to say about the matter, since the state is implicated in this whole affair. Savile was friends with the Royal Family and former Prime Ministers, some of whom have also been accused of horrific crimes. Ted Heath, Prince Andrew, these are hugely powerful and unpleasant people. Who knows how deep this all goes?

I don't think Starmer is to blame. This is way higher than him. Did Starmer keep his mouth shut for the good of his career and health? Maybe, but if that's true then so did a lot of other people, and I mean a lot.

The fault with Savile is the police didn't follow up on him
This isn't the fault of regular investigating cops. The fault lies with this who make decisions. Your guess is as good as mine when it comes to identifying who made the decisions. Someone, somewhere made the decision to not investigate Savile. That wasn't incompetence, it was to protect him. He was untouchable. This is what Starmer must have known.