They'll formally apologize, as talk is cheap, and then do nothing further.

And no, I'm not at all kidding or exaggerating: this is THE most common strategy in British Political and Social Elite circles for getting rid of such "problems" when denying it doesn't work.

Deny it, deny it was a problem, deny it was systemic, apologize and claim it was too long ago and it's pointless to do anything about it now, is a well travelled multi-step strategy in British politics (THE main strategy, even) to avoid actual consequences for their actions or lack of action.