If you don't already fill in a tax return you should call HMRC and tell them you have income from babysitting, and about how much it is. They may then decide to send you a tax return at the end of the year so you can put your babysitting income in as 'other income'.
You do not need to register as self employed for occasional babysitting: there is of course a grey area between a couple of evenings a month for friends and setting up a babysitting service with a web site, adverts in the local paper etc. when you would need to register as self employed.