Colin, you assume too much. I manage a coppice woodland that was profitable for the Earls of Darnley for hundreds of years. The coppice stools are hundreds of years old and there are some enormous standard trees, both the old standards and the coppice regrowth will suffer badly unless squirrels, and in the case of regrowth, rabbits and deer are controlled.
My woods border a 75 acre Woodland Trust area, I haven't seen any pest control there but it's "Amenity Woodland" and it doesn't need it, that doesn't stop hundreds of squirrels coming over the fence to dine on my Chestnut though. On another boundary there is a 350 acre "Community Openspace" owned by the Forestry Commission, it boasts the largest wildflower meadow in the South East, it also supports a huge rabbit population who spend the cold winter months digging up bluebells in my woods and nibbling bark from young trees.
I need pest control and regard it as part of managing a woodland for some income, the fact that I can get it done for free by a couple of retired chaps is a bonus that saves me considerable money.
If you still have doubts about the need to control Grey Squirrels I suggest you read this article on the Conservation Issues website:
http://conservation-issues.co.uk/Articles%20Pages/Grey_Squirrel_Article_07-07.htm
In particular, look at the sections regarding the destruction of rare woodland plants and the effects on native birds, also note that they have been placed on the global top 100 most destructive invasive species.