Yes, but only at certain times between November & March ... However there are doggy beaches ... Think there is one in Brighton !!! :)
Elwood Beach allows dogs between the rock groyne south of Point Ormond and the beach access ramp 35 metres south-east of Normandy Road (5.30 am - 9.30 am, 1 November - 31 March).
Brighton beach is all year round & a great spot for dogs, just down the round.