How Western Europe might relate to an imperial federation

Would Western Europe join an enduring British imperial federation's defence system?

It would probably form a separate but closely aligned European bloc rather than merge fully with the federation.

The imperial federation is more integrated than a conventional alliance, combining elements of collective defence and shared government. Its armed forces could operate through a common command even if national identities remained. Western Europe would probably form a separate grouping with a close relationship to that federation, while France would insist on enough separation to prevent the two systems becoming one organisation. Operational alignment does not require political union in this counterfactual post-war order.