Well I have played a few with British cast, and also UC3 had a section in London which was fun.
The Motorstorm series although set around the world had a LOT of Britishness in it, one of my favourite vehicles was based on a Bowler Wildcat, and the titles for Pacific Rift feature one of the Invincible class carriers.
I also theatened a boy who got stupid by mocking up the cover of an Eastenders game complete with Playstation logos, and telling him it would be his next and only game.
1) X-Factor First Person Shooter, where you shoot crap singers and Cowell.
2) SAS stealth shooter, you play as an SAS member.
3) An open world car game with European cars and you drive on the LEFT (Imagine Burnout Paradise with British and European exotica and you do not head on crash every thirty seconds), suggest idealised country A Roads, surrounding a modern city dual carriageways.
4) A tank game where you drive a Challenger 2 in the desert and wipe out all oncomers.
5) Eastenders FPS, in fact an FPS of any soap
6) 1980s cop game where you play a cop based on Gene Hunt.
I will think of more