I've heard squirrels called "tree rats" too. They are rodents, after all. Sorry to hear they are an invasive species in the U.K. Luckily for me, I don't have to travel far to encounter them. I only have to walk out the front door and there is usually one around. My favorite is a one-eyed male (named "Nelson", of course). Here is a photo of "Molly Jane". They'll eat peanuts right out of my hand. I have apparently spoiled them!