I still think it would be illegal for a state primary to introduce partially private funded places, but I'm no expert on such matters.
It is great if there are spare places, I think they have done everything they can to meet the high levels of demand for places.
Some people use childminders to help with pick up and drop off as well as providing the other half day child care. If shared with other parents at the nursery it is likely to be cheap than if paying a private nursery for the half day, so it can be cheaper - provided you can find a childminder you are happy with.
I should say, in case it is not obvious, that my daughter currently attends Fairlawn nursery and loves it.