For Enstone, there are two grass runways. The one south of the tarmac is part of the main operation and they would charge you as mentioned above.
However, the North side grass is operated by the maintenance base and they don't usually charge a landing fee. I don't know if they would encourage visitors just for circuit practice and the strip is a bit prone to water-logging.
So it may be worth checking with them.
If you don't mind going a bit further North; Hucknall has two very good, well drained grass runways and would charge very little (PPR weekends only).