The tax credits side of things is confusing and I don't understand it all fully. So this spreadsheet may give an idea as to the cost.
I did initially try to work out the grant and/WTC side of things but quite frankly it got too confusing.
From my calculations... based on a childminder charging £5 per child and only charging for 40 weeks per year, nanny costing £10 gross per hour and only requiring pay for 40 weeks plus statutory holiday,
Childminder: £12,800.
Cost of Nanny: £19,238. Note: Cost of nanny is different to nannies salary. Nannies salary in this case is £14,600 includes 22.5 days of paid holiday.
There are lots of if's and but's... for example you may not find a childminder prepared to work term time only, or you may find one who will but they will charge a retainer fee during school holidays. You may not find a nanny who would work term time only. A nanny may want less/more salary than £10 gross per hour (£14,600 per year based on 32 hours per week, 40 weeks, plus 22.5 days holiday). Are the misc costs I have added in for the nanny, things like activities budget, mileage, reasonable... they could be under or over estimated.
You also have the added problem of the possible need for two childminders, who may have different terms of business. The childminder who only provides after school care, may well charge a per-session fee rather than per hour, so £10 (£5 per hour) may not be the correct amount for the after-school care for each school aged child.
A big advantage of having a nanny is that the nanny would do all the running around between schools, rather than you doing it.
As you would be a student, rather than working, you may be better off claiming the Childcare Grant than childcare element of Working Tax Credit. If you are not working at all, I don't think you can claim WTC anyway so the Childcare Grant may be all you can claim - it may pay more, as the cap is £255 per week, rather than 70% of up to £300 childcare cost (which in your case caps you at £210 per week). However, how do you know if you would get the full £255 per week (during term time) of the childcare grant? I don't know how they work that out.
A nanny is going to be more expensive based on the information you have provided plus the assumptions I have made.
Given that the Childcare Grant is capped at £255 per week and that either of your childcare options will cost you more than £255 per week, you will have that other money to find. So if you are getting a loan for that, you probably want to go for the lowest cost option. I would suggest you keep looking into childminders and establish your costs for that.
I only thought it was quadruple as when I googled one site said you needed 32k for a nanny
That's quite cheap for a full time nanny (who could be working 60 hours per week, all year round). It could easily in my view cost that, however you are not wanting 60 hours, you are wanting 40 and only during term time. I think £20k would cover it.
Have realised I am definitely in the wrong profession though, sounds like being a nanny is quite a good wage!
It certainly can be a reasonable wage. Have to say I got paid more in other jobs, such as Sales & Marketing, IT Support, than I do now as a nanny. It's not the easiest of jobs, as you know having 5 children of your own.