If she has used all her allowance and her allowance includes bank holidays then no you shouldn't pay her but if it's so many days + bank holidays then you would I think? Obviously it's your choice if you want to pay her or not but I think that's how it works.
As employer I would expect you to keep track of holiday taking into account days you don't want your nanny to work. There is no right to have bank holidays off, they are normal working days. So if you want them to work then it is your choice. I would pay this time. I would then plan in future what days you don't want them to work.
Legally you may be do them unpaid but at this late notice I am not sure that is good for nanny:employer relationship. ACAS could give advice.
If your nanny is technically available to work on those Thursdays, but you don't need her, yes you need to pay her. It would be better if you could look into this at the beginning of the year and say 'you have x amount of days holiday, but 2 of those days should be taken on Xmas day and NYD'. I've had this in my contract before, where the family always went on holiday for 2 weeks at Christmas. However, this time I agree with nannynick that you should pay due to late notice, but implement this kind of thing for next year.