There are 3 premier sites with showers electrical hook ups probably even broadband these days; Hollands Wood Holmsley and Ashurst; we've been going to these for years and years (mostly Ashurst recently as it's dog free) even though the price has at least doubled since the C/CC took joint control of them. But even at £80 for a 3 night stay in August for 4 it's a bargain; I just love the place so much
Then there's Roundhill which is a sort of halfway house It has showers now; I believe it's the only one that accepts motorcycles or maybe it's groups thereof.
The others are all very nice and secluded have ridden thru most on the way into and out of the inclosures but have no toilets you have to bring your own and natch I've never tried any of them.
Hope this Helps.
ps You can usually turn up on spec at any of them apart from on Bank Hols and get in (Ashurst is always full late May BH but they always take the Full signs down on the Monday as half the people leave); if not they will direct you to the nearest alternative. There are a few private sites just on the periphary
in extremis.. These days it may be the case that you have to book online for the smaller sites as there is nobody on duty there out of peak season. A lot shut down after the summer and IIRC only one (basic no loos) is open all year round.