
You could try Seasalter, up Whitstable way. I've visited it in all seasons with any restrictions - the only bit to worry about are the beach huts, if you start at the Sportsman pub (opposite the caravan park). There's a lot of rabbits there, and this time of year (excepting smart people staying out of the rain :D) lots of people have barbecues there, very tempting for dogs! :p but there aren't many huts, if you go past them it's nice and quiet as the tourists tend to head the other way (towards whitstable). There is a sign that says 'private beach' just before the huts - you're allowed to cross the beach if you stay below the line of the sign.
Oh, it's a pebbly beach btw - but a lovely one :)