The 34th "Red Bull" Infantry Division was one of the earliest units to arrive in England. Also the 1st Armored Division arrived there and transitioned to the newer Sherman tanks. Both of these units were the first to be sent into combat in North Africa.
The 1st Infantry Division arrived early in UK, I believe.
Since the 34th Division fought continually in N. Africa, and Italy, it accrued more time in combat then the 1st Infantry Division, which was taken out of combat for training in preparation of the D-Day landings.
Custermen