Net pay is horribly complex to do when someone is not working full-time for you. This is due to them being highly likely to have other work on other days.
Net to Gross calculation is possible but is not an exact science. It is very hard to know what tax code would be used in the job you are offering.
Example - a job paying £300 per week:
If you assumed that all tax allowance was allocated (1000L)
£300 net per week = £358 gross per week.
If you assumed that 1/2 the tax allowance was allocated (500L)
£300 net per week = £386 gross per week.
If you assumed that none of the tax allowance was allocated (BR)
£300 net per week = £414 gross per week.
You DO NOT KNOW what tax code will be allocated to the job and the tax code CAN CHANGE. It is therefore not advisable to agree a Net salary.
Looking at your situation, lets say the nanny wants £8.25 per hour for working a 10 hour day. You do not know their taxcode.
At BR tax code, £8.25 becomes £10.31 gross.
At 500L tax code, £8.25 becomes £8.25 gross.
At 1000L tax code, £8.25 becomes £8.25 gross.
So does it cost you as the employer £8.25 + Employers NI, or does it cost you £10.31 + Employers NI? You simply do not know how much it will cost you.
The one thing you do know, is that due to the salary being £103 a week (this assumes a 10 hour day, that figure will be different depending on the hours), then there is no Employers NI due, as that is calculated on a Per Job basis.
If you agree a Net salary, you WILL BE paying the nannies Income Tax.
If you agree a Gross salary of £10.31 an hour, you would DEDUCT from the nannies salary their employee income tax and pay that to HMRC on the nannies behalf.
If you agree a Gross salary of £8.25 gross, you would DEDUCT from the nannies salary their employee income tax and pay that to HMRC on the nannies behalf.
So not sure what to suggest really... if your nanny insists on having Net pay, then use a nanny payroll company and be prepared to not know how much it will cost you - perhaps take the £10.31 figure as a guide.
With a Net Pay Agreement, if the nanny has a student loan, you may be paying back their loan for them! With a Net Pay Agreement any deductions from earnings such as back payment of tax, you will pay for.
So please try to agree a Gross salary with your nanny.
Your Nanny (not you) can ask HMRC to split their taxcode between their jobs. HMRC may or may not agree to do that and it will impact what their other employer pays if they have a Net Pay Agreement. Any split of coding may not result in you being able to pay the nanny a Net salary and have the Gross salary be the same... for example a code of 400L might be used, you just don't know.
MrAnchovy's PAYE Calculator - have a play.
Perhaps agree on a gross salary of £10 per hour. Then if they get allocated a taxcode of (for example) 400L, then their take home pay (net) will be more than they are expecting. If they get taxcode BR, then they will get a bit less than they expect.