We went to Warren farm campsite in Brean sands in Somerset,fab site,they have got about 4 differant fields just for dog walking,beach is just across the road and a pub,laundry,shop,fishing lakes in site.We will be going back next year.
If you're coming from Guernsey the one in Brockenhurst MQ suggests might be worth a look it. I have done caravan holidays with dogs but always mid/north Wales, so a bit far to travel for you I expect.