...OTH if Britain wouldn't have been a globe-spanning empire, they wouldn't have needed a more precise way to measure longitude, and probably wouldn't have invented it ;)
E.g. the Brits had built a whole government body around the task, which then resulted in a competition, with Harrison's chronometer coming out as winner:
The causality you gloss over seems to be more important than the causality you'd like us to focus on. The ships came first.
Empire -> need for chronometers -> chronometers.