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It definitely sounds implausible, but this lengthy article from a 1917 issue of War Illustrated makes it seem otherwise. While the article goes into quite a bit of detail on the military and political ramifications of a Channel Tunnel during WWI, how exactly would one go about getting the thing constructed before the war began? Were there any investors and financiers willing to back such a project, or will it have to be a government endeavor? Even with the Entente Cordiale in place, I don't really see a lot of cooperation between the British and French governments.