The clumber park site is lovely - we've been several times to the caravan club site although I don't think they allow tents on their own. There is a smaller tent site in the park but I don't know much about it other than cycling past it. Just beware we don't get any mobile signal there at all although it is beautiful.
You might want to think about Lincolnshire too - some nice sites in woodhall spa which we are looking at for this year (i quite fancy the Jubilee Park site) Pine Trees site outside Skegvegas has also been recommended to us by a friend although we haven't been yet.
I'm planning a camping trip with some friends. They live in St Albans, we are in York, so looking for somewhere roughly halfway. By my very rough calculations, this would be Leicestershire/Nottinghamshire.