Jeremy Tankard's work would be a good place to start...

http://typography.net/

Bliss might be a little too like Gill Sans for your taste, maybe Fenland would do. Or perhaps FS Elliot.

http://www.fontsmith.com/fonts/fs-elliot.cfm?tab=detail&

Tim

Recent + British = Tankard.

hhp

Another option is Houschka: http://www.g-type.com/houschka-pro-font.

Keith.

Yeah i've just been looking at Bliss by Tankard, very nice typeface.

Thanks

Priori Sans might also qualify as a "warped Gill Sans".

Here is mine...
http://www.impallari.com/cabin

Or... http://www.g-type.com/organon-sans-font

I like Camphor from Nick Job:
http://www.linotype.com/769290/Camphor-family.html

P22 Underground Pro Set
Nice alternative characters and diamond tittles!
http://www.youworkforthem.com/font/T0515/p22-underground-pro-set

I like David Quay’s Kade, but it is clearly a display face.

What are your criteria for British? --
Country of birth of designer?
Citizenship of designer?
Residence of designer?
Where the typeface was designed?
Country of publishing foundry?
Recognizable British look or design issues addressed by the face?

Please weight these criteria according to importance.