My calculations:
Currently you are paying £16,395 per year gross - £6.30 per hour.
She is asking for £20,163 per year gross - £7.75 per hour.
A comparison:
As a Level 3 qualified nanny (18+ years childcare experience) living 25 miles outside of London, caring for 4 children - two of whom all day, other 2 before/after school, I was on £7.33 per hour gross.
So I think that £20,163 is too much. You aren't in London and your nanny does not have lots of experience, or level 3.
You currently pay above National Minimum Wage, so legally you are fine (NMW applies for live-out nanny positions).
Are you able to get Childcare Vouchers from your employer when you go back to work? If so, may be worth getting your nanny to check that they comply with Ofsted registration requirements, and get registration underway. Then you could increase her salary, by say £800 per year, as I expect you would be saving around £900 using the voucher scheme (nanny registration costs £100). Savings Calculator - savings will depend on your salary.
If you were to increase salary to £17,195 gross, it would be around £6.61 per hour gross.
I wonder how it compares with other jobs in the area. Try searching NannyJob to see what nanny jobs are in the area. Some if you are lucky will indicate salary.