Hi Hannah,
Try these....
B.B.C Running Club
Barking Road Runners
Belgrave Harriers
Bexley AC
BP Running Club
British Airways AC
British Milers' Club
Brunel University AC
Crystal Palace Fun Runners
Crystal Palace Triathletes
Dulwich Park RC
Dulwich Runners AC
Ealing Southall & Middlesex AC
Ealing Sporting Candy AC
East End RRC
East Grinstead Triathlon Club
East London Runners
Enfield and Haringey A C
Eton Manor AC
Greens Health & Fitness Chingford AC
Haringey Jogging Club
Harrow AC
Hercules Wimbledon AC
Herne Hill Harriers
Hillingdon AC
Kent AC
London Business Houses AAA
London Frontrunners
London Heathside Runners AC
London Irish AC
London Vidarians Walking Club
Metropolitan Police AC
Metros RC
Newham & Essex Beagles AC
Orion Harriers
Parkside (Harrow) AC
Ranelagh Harriers
Richmond & Twickenham AC
Serpentine Running Club
Shaftesbury Barnet Harriers
Sheen Shufflers
South London Harriers
St Mary's College AC
Striders Of Croydon
Sutton & District AC
Thames Hare & Hounds
Thames Valley Harriers
The Stragglers
Time & Talent Trotters
Trent Park Running Club
Victoria Park Harriers & Tower Hamlets AC
Walthamstow Athletic Club
West 4 Harriers
West London Hammer School
Wimbledon Windmilers
Windsor, Slough, Eton & Hounslow AC
Woodford Green & Essex Ladies AC
I got this off the UK Athletics website, if you do a search for London it will list these and allow you to click through each club name for specific info on the club.
http://www.ukathletics.net/vsite/vnavsite/page/directory/0,10853,4854-164156-181373-nav-list,00.html