How would British control of Hawaii affect the modern British military and relations with the United States?
Short answerIt would redirect American Pacific basing - probably toward Guam or the Marianas - and create cascading political changes too large for a simple modern snapshot.
NotesGuam, the Marianas, Midway, Wake, and a retained Philippine base are possible alternatives to Pearl Harbor. Guam is the most plausible durable choice. The scenario also changes decolonization, Anglo-American relations, and modern operations in the western Pacific too deeply for a single deterministic outcome.