Here's some ideas for you, don't know if they are things that teenagers specifically like but are British. Also try looking under recipes and British cuisine on this site - there are loads!
Meals - roast dinner (pork, beef, chicken, etc), toad in the hole, fish and chips, shepherds or cottage pie, Lancashire hotpot, sausage and mash, pies (chicken, steak and kidney, etc), cauliflower cheese, cornish pasty, coronation chicken, kedgeree, fish pie.
Puddings - spotted dick, jam roly poly, apple pie, crumble, bread and butter pudding, trifle, treacle tart, eve's pudding, steamed or sponge puddings, apple charlotte, rice pudding, bakewell tart or pudding, brown betty, custard tart, eton mess, queen of puddings, gypsy tart.