I usually choose Special Operations Doctrine or Luftwaffe Ground Forces Doctrine and follow this build order:
4 Volks
Medic HQ Truck at HQ
Raketenwerfer
Infantry gun
Schreck up every Volks squad
Flak HQ
Luchs
Obersoldaten with StG upgrade or Falls
PIV or Command Panther
After you have secured your territory all your forces should be used to attack your foe. Make sure your Volks come as close as possible to Tommie squads and flank with your Sturmpioneers if the map allows it. Otherwise you have to wait for infantry gun to dislodge the Tommies in order to be able to start offensives.
Once you have your Luchs out be careful about the Sniper, AT guns or Bofors. Try to be as aggressive as possible since the British cannot fight on every front resulting into losses of map control for them.
+1
I've found facing a decent OKW opponent very difficult as the British, but then again I have little idea of what to do as the British.