During the u-boat peril (Battle of the Atlantic), the German navy never succeeded in strangling the import of goods to the UK and thereby forcing their surrender. However, Churchill remembered the u-boat peril as the only thing, which really frightened him during the war. Did the Germans really get that close to forcing Churchill out of the war, or was this just an illusion caused by the psychological effect of the war?

Edit: I’m aware of the significance of the battle itself. I’m interested in the role of the uboat, and how their actual damages live up to reputation.