Mediterranean routes and the wider war

Was Mediterranean strategy mainly about preserving the British Empire, or did it serve the wider Allied war?

Both. Securing Suez reconnected imperial routes and shortened the movement of Atlantic supplies toward the Indian Ocean and the Pacific war.

The Mediterranean was a route problem as much as a battlefield. Italian power threatened British use of Suez and forced traffic bound for the eastern empire onto the much longer route around Africa. Reopening the sea would let supplies from British, Canadian, and American Atlantic ports move through Suez toward the Indian Ocean and Southeast Asia without first crossing North America and then the Pacific. That shorter chain mattered to the long-term Allied war against Japan as well as to the defense of imperial possessions. Mediterranean access could also support assistance to the Soviet Union through the Middle East or potentially the Dardanelles.