train will be a pain and take ages. you should rent a car and go to Southend for flat lagoons or the southcoast for general/wavy conditions.
rent a car it will be easier, but remember average car will cost about £100 or $150 to fill up, but could get you 3 trips to the coast from London.
As regards cold, depends on what you're used to, it has been unseasonably cold last few months and hovering around 4 C, but minus with windchill. it should be a balmy 10-15 C soon.