Grey squirrels are vermin (rats with bushy tails) you are legally entitled to kill them In fact it is illegal to feed them You are allowed to catch them in traps but not to release them into the wild as they are not a native species.
My husband has killed 11 in our garden this year. If they get into your roof space they will do tremendous damage. They eat baby birds and birds eggs.
Daily mail - a couple of weeks ago a lady came back from holiday and one had come down the chimney it had eaten the carpet furniture all the window frames estitmated cost of damage �10,000 luckily she had closed the lounge door or it could have gone right through the house.