I am interested to see how you work things out... to see if the tax credits system will really enable parents to use a nanny, rather than childminder/nursery.
I think you have one child... is that right? Therefore if you qualify for 80% of childcare costs, the maximum weekly amount paid is £140.
If you were having a full-time nanny, working 10 hours per day, 5 days per week, earning £100 gross per day then weekly cost before Employers NICS is £500.
Yearly cost therefore £26,000 plus Employers NICs of about £2650, giving total you have to find from your take home pay of lets say £29,000.
Tax credits if you get 80% would be £140 x 52 = £7280, giving you £21,720 to pay.
If your pay was £29,000 per year, your take home pay would be £21,817 (assuming usual tax code), which only barely covers nannies salary.
Clearly those are probably not the figures for your case, but in the above situation, I can't see tax credits paying £7280 given the income level.
Don't suppose you would share details of your calculations, so that I and others can see how this does actually get calculated.