Unfortunately we have had the scenario of squirrels in the loft.
At the time the area was overrun with them and it took a determined effort by a number of nieghbours to deal with the problem.
We would not worry too much about them discouraging the birds. The problem is that they are legally vermin. It is not so long ago that it was the law that if you saw a grey squirrel you had to notify the police.
It is still illegal to trap them humanely and release them in, say. woodland.