What is Europe defending itself from exactly? Russia is a country in steep decline and Germany is committed to dominating the continent via non-military means. An EU military is a vanity project for offensive, rather than defensive, purposes. The minute it happens you can already tell they'll be sent to somewhere like Africa for peacekeeping or whatever, but in reality it'll be to show it off as a kind of perverse media stunt.
For the UK it's a different choice and we're already going further down the Anglosphere/CANZUK military route. Makes sense given we're already highly integrated with them (5 Eyes, TTCP, ABCA Armies, etc).