I'm pretty proud of my county's history... others seem to have covered many salient points, but it mostly boils down to the fact that being British is to be a mongrel. Our language shamelessly borrows and steal from whatever it can get its hands on. Our genetic stock is especially broad with our continued absorption and general tolerance for immigrants (sure, we ***** about them, but they generally don't get thrown out for it).
We're an adaptable lot- our Empire managed to evolve into a commonwealth instead of collapsing. We have some of the finest educational institutions in the world, we also essentially founded the basis of many modern constitutions and legal systems with the Magna Carta, Bill of Rights, and such concepts as independent judges and trial by jury. We've fought and both lost and won our fair share of wars, sometimes with ourselves. We sparked the industrial revolution and, to this day, continue to affect countries and cultures around the world.
Even the gaming industry owes a lot to us. DMA Design kicked off the GTA series and continue to make GTA games to this day as Rockstar North. Bullfrog gave us Populous, Syndicate and Dungeon Keeper, subsequently spinning off to form Lionhead who went on to make Black and White 1/2, Fable 1/2 and The Movies. Rare's given us GoldenEye, Perfect Dark and others, Psygnosis made a hell of a lot of Lemmings, Sensible Software gave us Cannon Fodder, Team17 infested us with Worms, The Creative Assembly are still making the Total War series, Criterion the Burnout series, and of course, there's Introversion with Uplink, Darwinia and Defcon. Eidos deserves a mention, for having published the Tomb Raider (also originally homegrown by Core Design), Commandos, Deus Ex, and Theif series.
Not bad for a country that only makes up ~1% of the world population.