Yeah, after decades of debate as to whether the Grey has or hasn't impacted the Red, there's now pretty much agreement that it's tended to drive out our smaller native Red. Added to which there's a virus that Greys carry but kills Reds (which is what wiped out 80% of the colony at Formby this year - tho', ironically, it's not strictly speaking a native being introduced from Eastern Europe, even if it is the same species!)
But the Grey is now under 'threat' from a new variant: a black sub-species which is larger and is in turn driving out the Grey (not that I've seen one - they're all grey here). Who knows, maybe in 10 years we'll be calling for the saving of the Grey (unlikely!)
Talking of American imports, another is the American Crayfish which is, surprise surprise, larger than our native and is driving them out!
We'll still take American $s though!