Contact a nanny payroll provider. NannyPaye and NannyTax are the largest providers in the UK, there are other smaller ones. Give a couple a call and see who you get on best with, ask them your questions.
The answer to your question will depend on whom you employ. If you employ someone who has no other income, then as you would be paying them £90 per week, you never hit the lower earnings limit threshold for class 1 National Insurance which is £112 (2016/17 tax year), £113 (2017/18 *to be confirmed in tomorrows Budget). In that scenario, you would not need to register as an employer.
If you pay them IN ANY WEEK the threshold amount or more, then you would need to register as an employer.
If this is not their only job, regardless of how much you pay them, you need to register as an employer.
Then depending on how much they earn you would need to deduct from their gross salary any employee Income Tax and employee National Insurance that is due, plus pay any Employers National Insurance due. If paying sufficiently high (£10,000+ per year) you will need to auto-enrol them in to a pension scheme - but as a new employer that would not start until 2018.
At first it all appears complex. Don't Panic! The nanny payroll providers will do a lot of things for you for a yearly admin fee. They will register you as an employer with HMRC, they will help with preparing a Contract of Employment, they will produce monthly payslips, or weekly payslips, and can offer you guidance on how to calculate holiday entitlement.
Holiday Entitlement for Term Time workers
You need to provide your employee with paid time off. With a term time only agreement, you may need your nanny to work the entire of term time and to only take holiday during school holidays. So you can calculate their total number of working days per year, then add on 12.07% as their Statutory Holiday or give more paid holiday than that. If they are able to take holiday during term time, then you use a different calculation... talk to your payroll provider.
My top tip... advertise the job with a gross salary. That way you can calculate your costs without worrying about what other work/income your nanny has elsewhere.
So... Don't Panic... call a nanny payroll provider, discuss your situation, ask about their fees including any additional charges for processing any changes to payslips, nanny leaving, nanny joining.