There's a related thread to this in chat today actually, here's what I said there:
On the question of proof, you don't need the perpetrator to be alive or to admit the allegations - both criminal convictions and civil claims can be upheld on the basis of less than 100% proof (beyond reasonable doubt/balance of probabilities respectively).
You don't need a criminal verdict to claim civil compensation - they are separate and independent types of legal action.
I think (but am no expert) that a victim seeking compensation from the estate of a dead person would have to start a civil case and show what financial loss has been caused to them, eg, the abuse means I didn't do as well at school as I should, so I have a crappy job instead of a high-flying career... But I can see that you'd need to start the case soon after death, because there might well be difficulties retrieving the money once it has been disbursed as per the Will.
Compensation would be claimed in a civil action (a civil claim is essentially a claim for money). The claimant would have to establish on the balance of probabilities that abuse took place and that they have suffered some form of harm as a result. It's not straightforward and would probably require a full psychological analysis of the claimant (victim), showing that the abuse had damaging consequences for the claimant's future life/prospects. If you're claiming against an individual then once they're dead, you need to claim before the estate is dissipated. In the Savile case, his estate has been frozen pending the anticipated civil claims.