Legally, they should be charging you any top-ups - it should be just as free at a private nursery as at state.
However, private nurseries are profit driven. If a nursery charges £4 an hour fees, but the NEG only covers £3.50 (can't remember exactly what it is) then they come up with as many slightly dodgy ways of ensuring they still make a profit off you.
Not all private nurseries, but some.