Can I use a Crossbow as a form of pest control against Pigeons in the UK or would the be classed as hunting & a breach of the Crossbows Act.

I work at a supermarket, and I often see the guys from pest control feeding the birds rat pellets on top of the roof. The birds often nest there, and make a mess. Is this legal, or is it animal abuse? Quite frankly, it disturbs me, and I hate to see it, but I don’t want to make trouble for my company, because they might fire me.