Yes and then no (or not without US help).

The British empire outproduced, manufactured, mined etc the Germans for basically the entire war. The question is more about why it took so long for the allies to get the upper hand.

The idea of ‘the plucky underdog’ is a myth, Britain was very much a superpower with a massive, resource rich empire behind it.

https://www.amazon.de/Britains-War-Machine-Weapons-Resources...

I found David Edgerton's "Britain's War Machine) (http://www.amazon.com/Britains-War-Machine-David-Edgerton/dp...) quit interesting.

He highlights that the Germans---far from the technical wizards they are often portrayed as these days---won in the beginning despite inferior material. The British and their allies always had material and technological superiority. (Lots of their gadgets just didn't work very well at the beginning.)