I think it was mostly in the American area but I don’t think they would have given Montgomery command over all forces during the battle if the British were not in it.
“Fresh from commanding the 21st Army group during the Normandy invasion, and having suffered an awful defeat in September as his troops attempted to cross the Rhine, Montgomery took temporary command of the northern shoulder of American and British troops in the Ardennes. He immediately fell into a familiar pattern, failing to act spontaneously for fear of not being sufficiently prepared. Montgomery was afraid to move before the German army had fully exhausted itself, finally making what American commanders saw as only a belated counterattack against the enemy. As the weather improved, American air cover raided German targets on the ground, which proved the turning point in the Allied victory. Monty eventually cut across northern Germany all the way to the Baltic and accepted the German surrender in May.”
http://www.history.com/this-day-in-history/monty-holds-a-press-conference