Agree a Gross salary, then you deduct Employee income tax and national insurance and pay those to HMRC. You also pay Employers National Insurance. A payroll company like www.payefornannies.co.uk can help you, or you can do it yourself using info supplied by HMRC, start by looking at PAYE Basics. You will need to produce payslips (if you use a payroll company, they will do that for you).
If you have not yet worked out rough costs, then you can use MrAnchovy's PAYE Calculator to get a feel for the likely figures. What you won't know is the nannies Taxcode and that could change during their employment, so for now use 810L which means that it take into account the full personal tax allowance. If someone wants NET pay, then use BR taxcode to give you the worst case figures, then calculate again using 810L.
Your home contents insurance policy will usually cover you having an employee. Some policies don't - so check your policy, for Employers Liability.
You should prepare a contract/written statement - see ACAS: Written Statement. This is a document that details your agreement with the nanny. Also look at NannyJob: Contracts
Remember that part-time employees get holiday entitlement... Minimum paid holiday is 5.6 weeks. So if the nanny was working 2 days, they would get 2 x 5.6 = 11.2 days per year of holiday at a minimum.
How many children do you have? The more children you have the more viable I feel a nanny becomes, as a nanny is not paid on a per child basis but on a rate set for caring for all the children in the family.