'non-imperial' is composed of the prefix 'non-' (from Latin 'non', meaning 'not') and 'imperial' (from Latin 'imperialis', relating to 'imperium' meaning 'command' or 'empire').

'imperial' entered English via Old French/Latin: Latin 'imperium' → Late Latin 'imperialis' → Old French/Medieval Latin forms → Middle English 'imperial' and then modern English 'imperial'. The prefix 'non-' has been used in English since Late Middle English as a negating element borrowed directly from Latin.

Originally the components meant 'not' + 'of or relating to empire'; the combined modern meaning remains essentially 'not relating to an empire' but is also used in broader senses like 'not grand/imperial in style'.