I live in the uk and I am considering caring for my 2 nephews during the day so that Mum can go to work full time. My question is, is it legal to accept cash for doing this?

If you are being paid, or receiving payment in kind, to do this then you MUST be a registered child minder to be legal.
It doesn't actual matter if they are relatives or not.

In the states, it is treated like babysitting/nannying. I accept cash when watching kids all the time.

Also, in the states you don't have to be registered for this. Not sure how it is in the UK though.