You assume that the UK, ON ITS OWN, could have inflicted enough casualties on the German U-Boat fleet to stay ahead of U-Boat production AND keep enough of its own merchant tonnage at sea to support its own domestic needs and defend its global empire. I'd like to see credible numbers to back that assertion. You also assume that the UK's military production could have covered its own losses on land, at sea, and in the air, let alone create a materiel advantage versus the Axis. No, it could not. Production figures back that up. If you look at the correlation of forces, simply based on domestic production during 1939-1945, the Germans were beating the British in most key categories. This also takes into account any curtailment of Axis production caused by Allied strategic bombing operations (which included tens of thousands of U.S. made and/or operated aircraft). Add in the other European Axis powers, and the divide widens. Look at the populations of the UK and the Greater German Reich. Once again, Germany had a significant numerical advantage. I don't think any serious professional historian on either side of the Atlantic would stake his/her reputation on the assertion that the UK could have beaten the Axis, or even just the European Axis Powers, without substantial U.S. assistance.
Second, although North Africa was a peripheral theatre, it was as mush a resource sink for the UK as it was for Germany. Furthermore, if the Germans hadn't had to worry about a possible invasion of western Europe, they would have been free to send more troops and tanks to Rommel. They also could have covered their transportation across the Med with fighters. It's entirely within the realm of possibility that, thus reinforced, the Germans could have defeated the Commonwealth forces in North Africa, thus taking control of the Suez Canal and thereby complicating things even further for the UK.
Anyway, if you believe that the UK could have done it alone, then there's probably nothing I can present that will change your mind.
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