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.

Is it possible to control the pest population of squirrels, rabbits, and pest birds with a crossbow? Or will this not work? Im pretty sure the rabbits are possible, but I don’t know about the squirrels and pest birds. If the answer is that it is possible, what bolt tips would be suggested for these kinds of targets?