that nursery manager sounds like a right battle axe and even if she was getting them ready for school, most of reception is about playing anyway.
Ds is in the nursery year at a state primary school. Their room has around 5 activities set out every morning (sand pit, some sort of sticking activity, colouring, building, puzzles) and in addition to that they have a book corner, an animal corner (snails, fish, hamsters), a dress-up place and a small room decorated in whatever theme they happen to be doing (so autumn I think). Also they have an outdoor space with a sort of shed that is either a cafe/garage/shop - that changes every couple of weeks and a play area with a play frame.
I went round about 4 or 5 before I found one I really liked so be prepared to look out quite a few. At least you know what you don't like now!