I Am Not A Lawyer But as none of the mumsnet legal pack have answered this highly topical question yet and I do have some knowledge...
This is a matter between the individual parents and their childminder, the Local Authority EHO, NCMA or whoever cannot tell parents they have to pay.
Contracts that run to dozens of pages often include terms that deal with this situation (known as force majeure - French for 'superior force'), but your childminding contract probably doesn't.
So if the contract doesn't help, hopefully the parents and the childminder can agree on something which they are both happy with - lots of unexpected things come up from time to time which require a bit of give and take from both childminders and parents. As a parent I would probably agree that if it was only a couple of days, I would pay. If it was longer than that (so I had to take unpaid time off work), I would not expect to pay for all of it. But if this became a big issue for my lovely childminder, I would not want to wreck our relationship over it so if she didn't see it this way, I would probably back down.
If the parents and childminder cannot agree, ultimately it would be up to a court to decide what should happen. The court is likely to decide that if the contract is temporarily 'frustrated' because the childminder (through no fault of her own) cannot fulfil her side of the contract by looking after the mindees, the parents don't have to fulfil their side by paying her.
If, as a childminder, you are not happy with this being the default legal outcome, you have two choices:
Amend your contracts to say that you should still be paid if you are closed down under certian circumstances (this is not easy because if you are too generous to yourself the terms could be judged by a court to be unfair and therefore unenforceable).
Get insurance which will pay out if you are closed down in certain circumstances. This is called Business Interruption Insurance (or sometimes Loss of Revenue Insurance).