Yes, and expect the Last Holdout Nation State in the 23rd Century to be reigned, but not ruled, by a sometimes dotty family of imported German Monarchs.
You've heard of the Space Hippies? You haven't lived until you've seen the 23rd Century Version of the Space Windsors...
Oh, of course, the only question left for England is this: have they made it past Andorra or a visiting Rigelian Friendly Team in World Cup Qualifying?
You know, from 2258 to 1966 is a really, really long time!
I see no reason why the Union Jack can't fly next to the Flag of the United Federation of Planets. I'm sure the United Kingdom still exists as a polity within the United Earth polity, which itself still exists within the Federation.
Though I, too, would have preferred to see the Flag of United Earth fly alongside the Union Jack and Federation Flag.
Also, I'm more bothered by the fact that the Union Jack seems to be upside down.
Typical American mistake by a bunch of Yanks from Los Angeles who think that just because they know some lines from the "Spanish Inquisition" sketch and the "Dead Parrot" sketch, they get to fly the Union Flag upside down.
Two words: "Jesus wept."