"I'm guessing as these are historic there would be no other evidence and determination of guilt would be based on whether they could prove that the accused is lying."
For a defendant to have to prove their accuser is lying sounds like a presumption of guilt - which is contrary to English law.
Often the prosecution's strategy is to convince the jury that the person was capable of the offence. For this they will present information about the defendant's life-style viz what they read, who they have known, etc.
They seem to depend on finding many people to make similar allegations in order to sway the jury by weight of numbers - even if many of the stories would not stand up in court on their own. A police tactic appears to be to publicise the allegations against a named person as widely as possible - in the hope of getting more people to come forward.
One court case collapsed when a witness said in court that his statement was a lie. He had only made it because the police had sought him out - and told him how much money he could get in criminal compensation. That compensation is only paid if the defendant is found guilty - which does give some concern for the accuracy of the historical facts presented by the prosecution.
Jimmy Savile's estate is subject to civil compensation claims by his alleged victims - probably using the civil "balance of probability" threshold. That would presumably be the case for any other alleged abuser who is dead - if the enquiry found they were likely to have been guilty in at least some cases.