The replacement of red squirrels by grey ones over much of the country has been shown to be at least as much to do with disease as with competition. Where the two co-exist, squirrel pox (probably brought in by the imported greys) can spread from one species to the other. It does not have much effect on greys, but is fatal to reds within a couple of weeks.
Further to past threads on red and grey squirrels, here is an interesting talk on how theoretical research has shown the best ways to try to slow the inexorable advance of the greys. Very watchable. (Don't panic - no need to do any maths)
www.youtube.com/watch?v=WVk6ubTNEoc
Iceland to offer over 60's a ten per cent discount