Hi, Clowes, Lypeat and Thornden wood just north of Canterbury is pretty dense but you need to ride up some steep hills to get to it. I don't know if you'll incur the wrath of the local council if you kipped in there but the odd night once in a while shouldn't be a problem. Failing that Larkey Valley wood South West of Canterbury on the Cockering Road running parallel to the A28 towards Ashford is also a good place. I've spent a few nights up there as a kid. Rather different nowadays though but if you're stealthy camping I doubt you'll be disturbed.
You mentioned the woods west of Canterbury. If you mean Bigbury woods, I think you'll find they get used quite a lot. Someone keeps reindeer up there in enclosures near the Chartham Hatch end and they're pretty picky about people being too near them. Given the choice I'd opt for Larkey Valley woods. You might get the odd horse rider there but it's pretty big and you can get off track easily enough to not disturb anyway.
Sorry I can't offer you a permission sort of place to camp. If I were still in the area perhaps I could ask around, but all my contacts are long gone now. I moved out of Canterbury 9 years ago and now I live in Normandy France.
Hope this helps a bit.