Churchill had a number of strategies for winning WWII.
Remember that there were a big set of battles in south-east Asia that the Brits fought mostly on their own. They (the Brits) also won North Africa on their own.
Of course, the “their own” means the British EMPIRE - with 2 million Indian soldiers (all volunteers) fighting for Britain alongside Canadian, Australian, South African and New Zealander troops.
I suppose you can say the Brits won North Africa on their own if you ignore Operation Torch, General Patton, the Kassarine Pass and subsequent operations.
About 100,000 American troops were not an insignificant contribution.