They carry a virus which has almost wiped out native red squirrels, they attack songbird nests and stop trees growing by stripping bark.I worked for most of my career in a college town covered with big, old (mostly) deciduous trees inhabited by a healthy crop of gray squirrels. The cute little rascals sure as blazes don’t stop trees growing, you’d be hard pressed to find a healthier stand of trees anywhere.
There is no shortage of songbirds in the town either. About a virus, I freely admit I have no direct knowledge. I’ve never seen a red squirrel there. The grays certainly appear healthy, the only dead ones I’ve seen were hit by cars.
I understand squirrels can be pests if they break into your attic, bury lots of acorns and nuts in your yard, empty your bird feeder or tease your cat. These, however, were not the reasons given for wanting them to stop reproducing in Britain.