I don't know if this will help but I consider myself to be a "much in with most things" nanny, I would for eg put your plate in the dishwasher!
I would happily, do children's laundry and ironing, sort through their clothes now and again (weeding out anything that's too big, too small, too worn) clean toys at end of day and periodically bin or out aside anything broken/not been played with, do a weekly shop, cook for the freezer, organise other people to come to house to do things like clean carpets/unblocks drains, pick up dry cleaning and probably some other things I've forgotten. Obviously cleaning up behind myself is a given.
I would prefer to do these things on my own time-scales though, if for eg if I think the ironing can wait till next week as X will be at a playdate/I wont be cooking a stew/the weather will be nicer etc and nothing is needed 'urgently" (ie uniforms)then I would prefer to leave it. (this assumes the pile getting bigger isn't causing anyone else any issue, such as being in a utility room).
I would not clean anything related to parents (one of items fine, regularly going through your laundry is not), ironing never (maybe something super urgent), cleaning (beyond after myself, I will hoover up glitter that may have been spilt but not the whole house). I'm not precious I just hate doing these sorts of things and love playing with children hence being a childminder (was a nanny) not a cleaner.
Having said that I would be flexible to some degree, if say you were selling your house and hadn't had time to hoover/clean something and asked me to give it a quick whip round just for effect that would be fine.
Could you get an Au Pair? Or what about shortening the nanny hours (or getting a new nanny who better matches what you need now) and getting a separate housekeeper.
Anyway, childcare.co.uk is great for finding childcare - I'm sure someone somewhere would be happy with this role. You just have to find them.