I thought the Battle of the Atlantic had swung in favor of the Allies by late 1941, a pattern only broken by U-boats preying on low hanging fruit before the USN got their act together. Were the U-boats still sinking more ships than were being built in, say, November 1941?
The Battle of the Atlantic, by late 1941 was very much a combined Anglo/American operation. U.S. bottoms made up nearly half the total tonnage being shipped and USN vessels conducted escort for any convoy including U.S. flagged vessels to mid ocean. The KM didn't have to sink every ship the British managed to acquire, just the majority.
Using the example I gave earlier, the British had 18.5 million tons of shipping to start the war, and could produce, with the rest of the Commonwealth, 3.5M tons annually. That wold mean that, by the end of 1942 total British shipping would amount to 29,000,000 tons, assuming no losses.
In 1939 losses were manageable, amounting to around 350,000 tons. In 1940 they were anything but manageable, reaching 3.4M tons (15% of the total shipping stock of the Commonwealth, including new construction, assuming no U.S. hulls had been allowed to enter the war zone) with a net loss of available tonnage of over 1M tons. In 1941 the figure soared to 4.3 million tons (close to 20% of the available tonnage), with a net loss of ~!1.3M tons. in 1942, a year that is impacted by "Operation Drumbeat" losses jumped to 6.2M tons (with the heaviest losses occurring AFTER the "Happy Time" including 755,000 tons in November 1942).
Between the start of the war and end of 1942 the KM had accounted for ~14 million tons of shipping, by all platforms, worldwide. The UK/Commonwealth, on its own could have had, at maximum, 25 million tons of shipping on hand/constructed during the same period, leaving, at best 11M tons (an additional 3M+ tons were lost in the first five months of 1943, enough to wipe out Commonwealth 1943 production for the entire year). Net losses of non-tankers to the UK merchant marine in 1939 to 1942 was 2,327 bottoms and 545 tanker bottoms.
Just to transport the minimum amount of oil from the U.S. needed to continue the war, not including oil obtained in the Middle East and shipped to Great Britain, required 4.5M tons of shipping. That would have left only 5.5M tons of shipping to transport EVERYTHING else needed, including oil from the Middle East being shipped to the Western Desert. Over the course of a year that means a total shipping of around 34 million tons (at 8 knots the Atlantic is BIG ocean, Slow Convoys took 15-18 days for one way transit and a cargo ship can carry roughly 1/3 of its rated displacement as cargo, faster ships were somewhat better, but each ship was good for around a trip a month). Just ration level food for the civilian population of the Islands came in at ~16M imported tons.
Without massive U.S. building of merchants, escorts and aircraft (all as part of Lend-Lease, which BTW was a really good deal for the U.S., considering) the UK withers on the vine no later than June of 1943.