The American red squirrel (at least the one in Alberta and western Canada) can subsist on spruce cones and twigs, and the bugs that use the spruce. The gray squirrels don't seem to use the spruce cones; they rob bird feeders and are ingenious. I have a supposedly squirrel-proof feeder but a couple of the greys have found a way- they are quite the contortionists. Tree difference may be the reason that they are separate in your area, Little Hawk.

About 1915, a man connected with the zoo released grey squirrels from the Toronto area in Calgary. They are now so abundant in the city that they are a nuisance to man and bird. There is talk of trying to shoot them out to reduce the numbers. They were also released in Vancouver.

Greys adapt to cities, are adept at climbing tall buildings and pester people eating lunch in parks. They gnaw holes in wood and nest in attics. Hand-offered food is accepted, but if the hand is empty, they bite to teach you to do better by them the next time.
If they interfere with the red in Britain, efforts should be made to reduce their numbers. It is always a mistake to introduce a foreign species.

The subspecies of red here in Alberta doesn't seem to invade houses for nesting purposes, but the one on the west coast does. My son and his family have a log house there. A red set up his home in an unused room, in a dresser drawer filled with old clothes. The mesh had come loose on a roof vent.