The English battle to get rid of this invasive species :
The Epic Century-Long English Battle to Rid Itself of American Squirrels | Atlas Obscura
The Epic Century-Long English Battle to Rid Itself of American Squirrels | Atlas Obscura
however the pine-martin has suffered at the hands of our gamekeepers/farmers for many years and it will take a big turn around with a lot of support from them to get them back.
Pine Martens are supposed to be extending their range quite rapidly nowadays. I think they could represent the only effective solution to the Grey squirrel problem with their 'natural selection' method of preying on squirrels- they could just succeed where all the other efforts and methods have failed, but they would need to be widespread over the whole UK to have a chance of success.