I think it's due in part to the parapox virus Greg, which the greys transmit to the reds. The greys are not affected much by the virus, but the reds succumb.
They also eat up most of the green acorns, leaving few for the reds (who cannot digest mature ones)
Where my sister lives up in Perthshire, there are quite a few red squirrels. It's lovely to see them, as I remember as a child watching red ones in the woods near our house.
House sparrows are getting a bit scarce here. I like the cheeky sparrows of all types. For some odd reason, my husband absolutely adores starlings and puts out food for them. They're just ordinary, boring birds to me, but he loves them!