You are allowed to kill the grey squirrel in the UK as they are vermin.
One of my neighbours shoots them, another traps them and then puts the trap in the water butt to drown them. You can also buy traps that kill the squirrel. All of this is perfectly legal.
You do not need to be licensed or authorised in any way to kill grey squirrels on your own land or with the land owners permission.
If you trap them you are not allowed to release them into the wild, as already stated.
I would not advise poisoning, as poison can be eaten by non-verminous animals, or the poisoned squirrel could be eaten by another species.