Well, we never really learn that one'd need to have warp in order to be a member, or a trade partner or whatnot. Or that one'd need to have specific civil rights or steer clear of abhorrent practices; Vulcans have duels to death at least.
And I'm not sure, but Malcolm Reed may have said that Britain still had a "Royal" navy. Suggesting that Kings and Queens were still the heads of state in Britain.
Or then not, as I could well see an organization preferring to keep "Royal" in the title well past the date monarchy expired. Unless it expired by going particularly sour.
In any case, that was before even the era of ENT; Reed's dad served in said organization, but was supposedly retired by the time of the televised adventures already. Our evidence for a (British? Australian? Dutch? Indian? Malesian? South Italian? Texan?) Royal Navy thus apparently predates even the final unification of Earth in 2150.