Have a look at campsite UK and use the map search, and also the campfire search, and the beach search.
Nearish the sea and allowing fires, if E Sussex is OK for you, look at Alfriston Camping, or Hawbush Farm, (eastbourne direction, I think) or Nr Hastings - Freshwinds, or in Dorset Riverside Lakes or Longthorns Farm?
I haven't been to any of these.