Churchill certainly won't like it, but he has a pretty limited control over things even compared to OTL: the French
Doesn't help a lot - infantry patrols are only effective quite a short distance in front of their own lines, where they have the effective ability to run away back to their own supporting units. Problem is, moving those supporting units forwards is rather hard.
Waiting until spring means a continuing cost in lives and money and risks either the German army re-establishing the front line, a new German regime resorting to desperate measures (gas) or Soviet intervention and occupation in the east.
A five mile per day advance for three weeks would lead to the entire German army being destroyed before winter.