I think you are misinterpreting the lyrics. I always understood it as a metaphor, that being Jerusalem used as
metaphor for the holy kingdom of God that would be planted on England's shores through the efforts of Christian evangelism (and/or social reform, given the 'dark satanic mills' and 'chariots of fire' reference) ... Why else would they ask if Jesus (lamb of God) walked in England? It's absurd question except as a metaphor.
I am unaware of what you mean by identity movement, so forgive me if others have picked up a different meaning, i'm just saying that wouldnt be the meaning the author intended.
Also, it's hardly a nationalist song (like "Rule Brittania!" is), but I guess it got some patriotic cachet from the "England's green and pleasant land" reference.
I am a Noachide, which means I reject chr*stianity and accept the Jewish concept of G-d, so I cannot identify the Kingdom of G-d with chr*stianity. Maybe that's coloring my perception.
But mostly I'm a literalist, which means that "Jerusalem" means "Jerusalem," just as "Israel" means "the Jewish people."