Finally obtained a copy of Harry Harrison's 'A Transatlantic Tunnel, Hurrah!' (1972, this ed. 1983).
Set in an alternate reality where America never left the Empire. "In charge [of the tunnel] is Captain Augustus Washington... A man to whom success will mean the final erasure of his family shame..."
Was told by the person who gave it to me that "the cover is very misleading".
@PMKeeling I think I read this back in the 80s when I was working my way through the library Scifi shelves.