Managed to defeat the British Commonwealth?
Not ever.
Germany was bankrupting itself paying Russia for resources. Indeed, one of the primary drivers for the timetable for Barbarossa was so Nazi Germany could skip out on paying Russia for the resources. I don't remember the exact numbers, Germany couldn't make those payments to Russia and maintain their army.
Even without Germany invading Russia, the British Commonwealth could have defeated both Germany and Japan -so long as Japan kept up its dream of conquering China. Japan was badly overstretched when it made the gamble for British Asia. When the British surrendered at Singapore, the Japanese artillery was down to less than ten rounds per gun. The road and transportation network in British Asia after they finished retreating back to India following the fall of Singapore was so bad that even if Japan possessed the resources sufficient to contemplate a full scale attack on India, it is doubtful they could have kept their troops properly supplied.
It is important to remember that at the beginning of WWII Britain was arguably the strongest country in the world with a colonial empire that covered a quarter of the globe and ruled 1/4-1/5 of the worlds population with an economic and trading network that had influence across the globe. Britain could simply afford to wait and let Japan, Italy, and Germany bleed themselves dry. It would have left all involved countries in ruins and caused millions more deaths, but it could have been done.
I should really start meditating on the regular.
