Tucked somewhere in a cabinet in most charity headquarters there’ll be a ‘risk register’, a document scoping out threats to that charity’s survival – say running out of money or losing key staff – and how to prevent the whole business from taking a nose-dive if they do transpire.

Accounts show somebody at The Jimmy Savile Charitable Trust had the foresight to prepare something like one of these.  But whatever disastrous scenarios it did highlight, they almost certainly won’t have run to the trust’s namesake being labelled a paedophile, and, with last week’s allegations of exactly that, the document will be worth comprehensively less than the paper it's written on.

Charities don’t come back easily from this kind of thing - and the Jimmy Savile brand has not so much taken a nosedive as combusted mid-air.

To their merit, trustees seem to appreciate this. Any future fundraising was immediately nixed by Dr Roger Bodley, a trustee on both of Savile’s charities, who gave the indication he’d be happy to wind them up and, to "amend and atone", spread the money between organisations that help sexual abuse victims.

A sound idea, most would agree, but one that won’t be easy to carry out.

As Dr Bodley hinted, abuse charities might not want to accept sums tied in any way to the Savile name – raised, if not directly by him, then under his umbrella.

Abuse charities might not want to accept sums tied in any way to the Savile name

There is an awkward symbolism to consider here. If reports are to be believed, the late DJ’s brand of abuse had a chillingly transactional nature; Elvis badges, and other gifts were apparently offered in exchange for sexual favours – tiny sums of hush money to add to the institutional unwillingness to listen to stuttering confessions on the part of young girls.

If abuse charities do take money, then – would they be nudged into similar silence on Savile’s alleged crimes, or even be colluding in a bid to repair the name?

These anxieties are legitimate. They’re even the kind that could encourage CEOs to block their ears to the anxieties of their accountants and take a stand on principle – for poorer, for better.

But in this case they should relent, for two reasons.

First, the money at the disposal of Savile’s charities has been doing little good for at least the last five years.

Despite Dr Bodley’s claim that beneficiaries will “lose out” if the Savile charities have to shut down – accounts of the Jimmy Savile Charitable Trust show that in 2010 the organisation, which has reserves of over £3.5 million, gave away just £35,000 pounds and incurred “expenses” of £25,000 in doing so. This pattern of meagre activity at high cost (even though none of the trustees receive a salary), is repeated to varying degrees in all the accounts since 2008.

This is not criminal, or even that rare. It’s just lax. It means the charity lacks the ambition to make a real difference. So, somebody should spit on their hands, and shunt the money over to others who can put it to better use.

The second reason abuse charities should accept the cash is more abstract. While there are times when money does go “bad”, when it becomes “blood money” – this is not one of them.

A golden donations rule for non-profits in the developing world goes something like this: “don’t take money from any person or organisation who, at the same time as giving to you, pursues activities that harm the people you’re trying to help”. While of course the victims of abuse are often haunted for a lifetime, Jimmy Savile is now dead, unable to cause any further harm whatsoever.

So, wrap it up folks. Close down the Savile charities, honour those who worked on them with good intentions, and, at the same time, right some of the wrongs that Savile is alleged to have committed.