Lets say you can agree a salary of £18 gross.
8 hours x 5 days per week = 40 hours per week. 40 x 52 = 2080 hours per year.
£37,440 gross per year salary.
Employer pension contribution (3%)= £1123.20 (may be lower than this depending how payroll is done)
Payroll admin & contract=£250
Activity budget: If it was £5 per day then £1200 per year (48 weeks).
If nanny uses their car to transport your children you pay mileage. £0.45 per mile. An average mileage of 60 per week maybe about right, small journeys add up. It can help to track your own mileage in your car for a while to get a reasonable view of what average mileage might be. 60 miles per week, £0.45 per mile, 48 weeks = £1296
If nanny does not use a car, will there be public transport costs, taxis/Uber etc?
Employers National Insurance: £3911
Then food whilst nanny is on duty (so probably lunch and afternoon tea depending what time your children eat in the afternoon/evening).
So rough cost to you as the employer is £44,097 so perhaps budget around £45k.