None of these are right by the sea, but look at Freshwinds close to Hastings and Pett Levels. Nethergong Nurseries by Herne Bay, or further afield White Meadow or Lower Lepe in Hampshire.
There is a Camping and Caravan Club site at Folkestone,it overlooks the sea. I believe it does not take caravans,
There is Caravan Club site, Black Horse Farm at Densole which has a tent area. Its not far from the coast.
I doubt they would allow fire pits but bbqs yes!
------------- DS-There's more to life than football!!!