Despite the inherent danger and the ticking clock, the Brits ventured in and managed to navigate the submarine, a terrifying and panic-inducing environment even when it's not about to sink, you're familiar with the layout, and your bitterest enemy isn't actively trying to explode everything. What's more, their horror trip was successful: The rescue party poked out with the Enigma Machine and all the necessary documents ... only to spend some terrifying time out in the open, with wind and waves rising, when the Bulldog had to temporarily leave them to investigate a potential U-boat sighting nearby.
When the Bulldog returned, this left just one major problem: Against all odds, the U-boat stayed afloat. Obviously, the Germans couldn't be allowed to see that, because even the most incompetent commander could probably figure out that a floating sub-husk with a missing code machine probably necessitates a whole new set of codes, stat. So the Brits hurriedly strapped the U-110 in tow and started hauling ass, at which point the sub, which had clearly been biding its time for maximum comedic effect, promptly solved the problem by sinking beneath the waves before the British could get her to England.
Sadly, "Yakety Sax" wouldn't be written for another 20 years, so they had no appropriate song to play.
The Enigma machine was turned over to the minds at Bletchley Park, and the war was arguably shortened by years. Now, just recast all those pesky Brits with Americans and you've got yourself one hell of a movie.