Here's a list of links to UK based improv comedy (and theatre) groups:

Newcastle:

The Suggestibles

On The Spot

Durham:

ShellShock!

Manchester:
ComedySportz

Liverpool:
Impropriety

Sheffield:

The Antics

Nottingham:

MissImp

Edinburgh:

Improverts

Cardiff:

Ludus Ludius

The Glamorgan Improv Troupe
Slow Genius

Oxford:

The Oxford Imps

Bristol:
Instant Wit

Southend:
Scared Scriptless

Hampshire:
Instant Soop

Brighton:

Noise Next Door

London:

British Comedy Invasion

The Comedy Store Players

The Crunchy Frog Collective

Fluxx

Grand Theft Impro

Improbable

Impropera

Kevin Tomlinson

The Ministry

The School of Night

Showstopper

The Spontaneity Shop

Sprout Ideas