His proposal for a new airport on an island in the estuary of the River Thames estuary — immediately dubbed “Boris Island” — was rejected. His plan for a hybrid park and pedestrian bridge across the Thames was scrapped after $48 million had been spent.

He championed a cable car across the Thames that cost about $80 million but is lightly used. He backed the design and purchase of a fleet of custom buses for London that were expensive and have had mechanical problems, and his successor as mayor, Sadiq Khan, stopped buying them.

But if Mr. Johnson is known for bold new ideas, in this case he has reached back to a bold old one. Engineers, business moguls and government officials have talked about Channel bridges and tunnels since the Victorian era.

In 1930, the British Parliament only narrowly rejected a proposed tunnel, and in the 1960s, officials in both countries confidently declared that construction of some kind of crossing was imminent.

But in an island nation whose best defense against continental armies has always been the Channel, generations of military and political leaders saw proposed bridges and tunnels as potential invasion routes. Lately, the Channel Tunnel has beckoned intruders of a different sort: migrants from Africa and the Middle East hoping to reach Britain.

Proposed Channel bridges have, at various times, been dismissed as possible threats to navigation. (The Dover Strait, at the Channel’s narrowest point, is one of the world’s busiest shipping lanes, currently used by over 400 commercial vessels a day, according to the British Maritime and Coastguard Agency.) And even when the political will existed to build a crossing, coming up with the money was always a challenge.

The Channel Tunnel, opened in 1994, cost more than $10 billion to build, and was not heavily used at first, raising questions about whether it was worth the expense. But it now carries more than 10 million passengers and more than 20 million tons of freight annually.