Anyone who is self-employed sets their own terms and conditions. It's very difficult to be a self-employed nanny, because you will want her/him (not a substitute, as eg a plumber might send another plumber) and you want them at a set day/time (not eg 3 hours a week, when it suits the nanny.)
I think you need to check this with HMRC, could be you're one of several employers of this "self-employed" nanny, which gets difficult re tax.
The fee they charge should include provision for not earning when they take a break. They set their terms of business, so you need to do whatever that says. If they don't work, they don't get paid. You could pay a bonus at xmas perhaps.
I would recheck that with HMRC. Nannies do not tick most of the boxes in the SE checklist. You require them personally to do tasks that you set out at a time and place of your choosing. Even in a FT (37.5 hours) job there is time to take on additional work. It doesn't change the emolument status of the person.
As in she's from a recruitment agency or she's from an agency which offers an employment service so she's employed by them. They do exist although they're rare and you would be paying them an all in fee rather than the nanny. A nanny recruitment agency should be advising you that you are the nanny's employer or they aren't doing their job correctly.
The usual exceptions are nannies in continuous temp employment like maternity nurses and those who do very as hoc work.
It depends on the agency as to whether they have correct info or not. My local council have a matching service and that tell nannies to be self employed, I have tried to correct them on the issue but they still say it. I even asked my local hmrc office to call them as it was worrying how not seriously they were taking it.