Where can I find a before and after school nanny?
Nanny Agency
online recruitment websites such as NannyJob.co.uk, Childcare.co.uk, Gumtree.com, FindABabysitter.com
They charge per child per hour?
No. Nannies charge on a per family basis. It could be per hour... though it's you who determines how much you pay, as you offer them a salary.
Do they cover school holiday?
They might or they might not. It will depend on the person and your contract with them. Some people may only be available during term-time, others may be able to do more hours during school holidays. Keep in mind that they may have another job during other days/hours.
How much in London?
Very hard to give any salary indications. Think about how much you are able to offer, then start advertising at a little below that so you can give a pay rise later on. In London nannies can be wanting anything from £7 to £15 Gross an hour.
Do I have to go through nanny tax etc and NI as well?
Yes you are the employer so you will need to operate PAYE. You don't have to use a payroll agency, HMRC do provide you with website & CD-ROM to help with the form filling. However it can be easier to have someone else do a lot of it for you... payroll agencies often charge around £125 a year... PAYEforNannies, NannyPAYE, TaxingNannies are just a few of many companies offering a service to parents.
As your employee your nanny is entitled to 5.6 weeks paid holiday (this can include bank holidays) plus they have other employment rights (such as maternity leave, redundancy, notice periods). Best advice is to treat your employee as you would want a great employer to treat you.