A nanny for 10.25 hours a day is going to cost you way more than £35 a day even if you can get a nanny to work at quite a low salary.
Term time only care adds to the problem as what does the nanny do during school holidays? Whilst they may get some other work, they may not, so you would need to find someone that suited.
How many weeks is term-time? It does vary, though maybe 39 weeks is average. You then need to add in holiday entitlement and calculating that is more tricky for term time positions than an all year round position.
I think holiday would be 12.07% of working time, so:
10.25 hours per day, x 5 = 51.25 hours
51.25 hours x 39 weeks = 1998.75 hours (per year)
1998.75 x 12.07% = 241.25 hours
So holiday entitlement of 241.25 hours (a bit over 23 and a half days), this can not be rounded down.
Total paid hours per year: 1998.75+241.25= 2240 hours
So if you could find a nanny who would accept £8 gross an hour (which may happen though many nannies I feel would want £10 gross, though your location may mean people accept less), then
Gross salary: £17920
Employers NI: £1410 (Calculation by MrAnchovy's PAYE Calculator 2013/14)
Then you have activity costs, mileage payments and perhaps factor in the cost of elec/heating being used during the day at your home.
So it will be easily £20,000 a year... probably more.
So I would say that is over £100 per day that childcare is provided (39 weeks x 5 days = 195 days of childcare).
Other options, a childminder - some may consider starting at 6.45am.
Think longer term... what happens when DD goes to school... then you may need before and after school care. Some nannies provide that, many childminders provide that.
So I would say, look at childminders... would any consider doing the start time you need?