This is not an exhaustive list, but is intended to be an index of all local and regional Drupal user groups across the UK. Feel free to edit.
England
East
Cambridge - http://www.meetup.com/drupalcambs/
East of England - http://groups.drupal.org/east-england
Norwich - http://www.drupal.org.uk/user_group/drupal-norwich-user-group
London and South East
Brighton - http://groups.drupal.org/brighton
London - http://www.eventbrite.com/org/61878136?s=6071340 | http://www.meetup.com/London-Drupal-Pub-Meet/
Oxford - http://groups.drupal.org/oxford | http://www.meetup.com/Oxford-Drupal-Users-Group/
Midlands
West Midlands - http://groups.drupal.org/west-midlands-uk
North
North East - http://www.drupalnortheast.org.uk/
North West - http://nwdrupal.org.uk/
Yorkshire - http://groups.drupal.org/yorkshire
South West
Bristol & West - http://groups.drupal.org/bristol-west-uk
Dorset - http://www.drupal.org.uk/user_group/drupal-dorset
South West - http://groups.drupal.org/south-west-england
Northern Ireland
Listed under Drupal Ireland: http://groups.drupal.org/ireland
Scotland
Scotland - http://groups.drupal.org/scotland
Wales
Wales - http://groups.drupal.org/wales-uk
Feel free to edit this article: do not remove groups and try and keep it in alphabetical order. Preferably list the groups.drupal.org site for a group. Commercial organizations are not to be listed here.