On the other hand, if it is a 'one off' - say you are going to a wedding or a training course or anything you don't normally do, and are asking your local teen who normally sits for you when you go out to look after the dc for the day, and aren't looking for structured childcare, then it would be a lot less.
It will depend on how many dc you have, and ages, but U18s Min wage is £3.79 and for 18 - 21 yr olds is £5.13, so my 16 yr old would be more than happy with £35 for the day and my 18 yr old probably would too, to be honest, as, by the time he's had to pay train fare into the shop where he works, it takes away an hour's pay, then as long as you don't have 6 high maintenance dc he's be happy to play with the dc, watch a bit of tele, go to the park, etc, rather than "working" in a shop for £46 less a fiver for his train fare.
That's not to say a trained nanny should work for this, but my interpretation of your op isn't that you want regular childcare, it's more of a "what should I pay my babysitter for a one off, longer sit?"
As I say - will depend on how many children and how high their needs are though.