A rabbit is a rodent, too. I've eaten more than my share of game, but I don't like it. Somehow, I can't see Brits warming to squirrel.
As for the red squirrel/gray squirrel thing...it's true in the States, too. More grays, fewer reds. Since they don't know what's going on with that, I think it's unfair and unscientific to assume the grays are pushing the reds out in some way. It may just be that the habitat is shifting in ways the favor gray squirrels.
Anyhow, the reds are adorable, but they're nasty, aggressive little bastiches. I had one follow me through the woods once barking at me.