I remember someone posting links to their camping blog last year and she recommended a site somewhere down that way where you could rent one of those folding fire pit thingies, or take your own. I remember I liked the look of the site because it's quite near to some friends of mine. I can't remember the poster's name, or the particular location, or find the thread. It may have been deleted I suppose.
Hello, twas me! I was going to suggest Britchcombe but I see you've already looked there! How about Turkey Creek - composting toilets kinda place. www.turkeycreek.co.uk/, oxfordshire. Otherwise perhaps head towards New Forest, I came across this one recently www.fishpondsbottom.com/ one of very few in the area that allow campfires!
I love Britchcombe - but "Decent loos and showers" are not there
They have perfectly clean portaloos everywhere (with paper/soap/mirror in each) and a few showers in a portacabin at the farm - where there are also 2 flushing loos. The owner is a wonderful lady (Marcella - hope she is still going strong) and the views and walks are amazing.
hillbilly I have just been to Inwood and it could be perfect for your between bath and london conumdrum. If you stay in the field closest to reception there are decent toilets and showers - not plush to be fair, but kept clean and perfectly reasonable. We live in Bath and it took us 1.5hrs to get there, access from London just down the M3. We thought it was amazing.