Right. Then the Leyland wins, though that with its two "Mk" it is cheating too
After some stretched limousines, we have :
Land-Rover
88'' Series III County Station Wagon (36)
Vickers-Armstrong
Infantry Tank Mk.III Valentine Mk.I (35)
some cars with long name due to the body type rather than the real model (e.g. Citroën 10 Conduite Intérieure Commerciale or Triumph Vitesse 1600/Sports 6 Convertible)
further we find a Harley Davidson
Ultra Classic Electra Glide 1450 (32)