Is Wareham Forest near enough? Great facilities including a pool. If you don't need hook up you can camp right in the forest away from the rows of caravans. Short drive to crabbing at Swanage. It's quite expensive as far as campsites go though.
How about Longthorns Farm. Beautiful site, close to Lulworth Clove. Brand new shower/toilet block which I'm reliably informed by someone on here is good. You can have a campfire. There is lovely woodland, stream, rope swings, alpacas and horses in the adjacent fields. Generally a very pleasant place. Review I wrote with lots of lovely pics here
Just to update, we went to Wareham Forest for 2 nights and it was amazing. The shower/washing up blocks were clean, the pool was amazing and we did a fantastic nature trail around the park. We were lucky enough to be mid-season so it was only £44 for 2 nights for 4 of us which as it had a pool I think is a bargain.