Some costs to think about.
Using a nanny payroll company to calculate the payslips and remind you of when to pay HMRC, plus provide you with any help you need regarding employing a nanny... £180-£276. You won't need to provide a pension scheme at this time as you are a new employer, you will need a scheme in place for 2018. www.nannypaye.co.uk www.nannytax.co.uk and others provide nanny payroll services.
Contract of employment... either use a template document such as from www.nannyjob.co.uk but do make sure you know how to write contracts as template documents do tend to need some adaption, or the nanny payroll provider will be able to provider a bespoke contract (cost varies).
Your nanny will be entitled to a minimum of 5.6 weeks paid holiday. So 5.6 x 10 hours = 56 hours of paid holiday per year. You can dictate when all that occurs but it isn't very nice to do that, so what often happens is that you decide some and nanny decides some. Consider if they will ever be needing to work on a Bank Holiday, if not and if that occurs on their normal working day then they take it off as part of their annual leave. Is the 10 hours all one day, or is it spread over several days?
Employers liability insurance - you should already have this as part of your home contents policy, check the wording. If not, then it is available as a separate product for around £100 a year though do check with your home contents provider first as they may be able to add it to your existing policy for less.
Consider any non-taxable payments such as nanny using their car to transport your son. Mileage rate up to 45p per mile is non-taxable. Mileage rate is only payable on work travel, not the commute to/from place of work.
Also look at activity costs - toddler groups, swimming, museums & castles, whatever nanny will be doing with your son.