Welcome to UKCS. There’ll be dozens if not hundreds of sites, you need to say where you’re interested in. I could list very many (if I had time) but they’re independent sites not CLs or CSs.
If you use the Site Search, you can limit it to CLs & CSs and tick on “dog walk from site”. But it’s not a perfect tool. I’ve found it can seem to apply only if it’s in the site ownership or control (a wood beside the field, for example). Conversely, several sites had a dog walk listed (hence our choosing them) but the walk was along a busy road verge. I know dozens of sites where we can walk straight from our pitch into off-lead areas, but they’re not listed as such in the directory.
Still no reply. We are at a CL now, Carefree Nurseries at Titchfield which has a dog exercise area. I chose this site because the reviews state that you can see the shipping in the Solent. You can't, the hedge is too high which is disappointing, but that's another story.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.