You determine the rate of pay, not the nanny. Whilst there is some negotiation, you are offering a job and they are either accepting the job or not as the case may be.
watfordmummy - do not agree a Net salary. The nannies taxation situation could change at any point and that will then affect the tax/ni payable. So agree a Gross salary with your nanny.
If your nanny wants to get currently around £10 per hour, you need to know what their taxcode will be when they are working for you.
Have they given you a P45 or completed a P46? Do you have any knowledge of them having any other income?
www.mranchovy.com/calc/ will do Net to Gross calculation. However you need to enter a Taxcode. If this will not be their ONLY JOB, then you may need to assume a taxcode of BR, which means all the income is taxed.
If they were say doing 15 hours a week for you and you wanted the Net pay to be roughly £10 per hour... then using MrAnchovy's calculator, I get £13.08 gross per hour - for 2011/12 tax year, using taxcode BR.
Next tax year 2012/13 using £13.08 an hour, 15 hours a week, taxcode BR, I get £10.06 Net.
And yes, it's a part-time job, so you would be operating PAYE most likely. There are some circumstances under which you may not need to operate PAYE, such as the pay level being very low and it being the nannies only job, but if you are paying £13.08 gross and hour and if it's 15 hours a week, then there is Employers NI to pay on that, so you need to operate PAYE.
For more information see HMRC: Employers' Responsibility For PAYE
Contract wise, I suggest checking you are covering everything needed in the Gross Misconduct section as Template Contracts can be a bit lacking in that area. This discussion from last year about Gross Misconduct is well worth a read.
Also if you are using a template contract, do check that the holiday entitlement is correct. BusinessLink: Holiday Calculator you can calculate in Hours or Days. If your nanny might work different hours at times (such as during school holidays) then you may need to use the Casual/Irregular method for calculating holiday.