A Transatlantic Tunnel, Hurrah! (aka Tunnel Through the Deeps) is an alternate history. Harrison began by positing two changes which would've allowed this changed history to exist. In this story, set in an alternate 1973, Washington lost the Battle of Lexington & was executed as a traitor. America remains a British colony dreaming of independence. The other change is that Columbus didn't discover the Americas & the cultures of South America weren't destroyed.
Thus Harrison brings into being a British Empire which has survived into the 20th century still influenced by its Victorian creators. But this ideal is threatened by increasing unemployment & the threat of economic decline. The empire needs something to boost its fortunes. So is born an engineering project to link Britain with its colony: a tunnel beneath the sea. Employment will increase & manufacturing will prosper.
The hero of the story is Captain Augustine Washington,engineer & descendent of the traitor. As well as wishing to see the tunnel's success, he wants to see his homeland achieve independence, or at least the dominion status of Canada & Australia. He's also in love with Iris, daughter of the genius behind the project, Sir Isambard Brassey-Brunel, who despises the upstart colonial engineer.
A Transatlantic Tunnel, Hurrah! is a curiously transatlantic book. The hero is an American, seeking independence for his country, but the British here are benign imperialists.