Re: shooting with air rifle. Yes, illegal in these circumstances. And you could fall foul of other airgun laws... If on your own property then if you fire a pellet and it leaves your property then you are committing an offence. Note that even low powered airguns are considered to be firearms. If someone saw you taking pot shots at pigeons and objected and reported you then yet again you are likely to get a visit from the boys in blue ... it has been known to be the armed response unit. So ... my advice is to forget trying to shoot them with anything other than a water pistol. But for a better solution, get some of the spiky things, plastic or metal are available from ebay and come complete with stuff to stick them down. We use then on a pergola with great effect.
Cheers, Phil