Are there any laws that I can be armed with when making a complaint to the police about a neighbour who kills wood pigeons. The poor birds sit in a large beech on the fence line of our properties, in an urban area of London (the neighbour attracts them in with bread) and are then targets for this man's air rifle. Apparently he cooks them to eat. Complaints have been made in the past but it has not detered him. Very often he only wounds and once the bird did not fall but was trapped by the branches until it was dealt with by crows.
Unfortunately he is strictly speaking within the bounds of the law. The law against discharging a firearm near a property not belonging to the firearm's owner only applies to gunpowder based firearms and not to air rifles. He is only breaking the law if the pellets go over the boundary into your property. Also, whilst it is against the law to brandish any firearm in a public place, he is perfectly within his rights to do so on his own property, even if the area in question is in the public view.
Feral (urban) pigeons are legal game with an air rifle. However, eating them is highly inadvisableas as they carry many diseases and parasites. So more fool him. The only thing you could probably get him on if the pellets aren't landing on your property is his bad hunting etiquette. From your description the way he is dispatching them is quite inhuman and not what you'd call a 'clean kill'. Whilst this isn't strictly speaking illegal in itself, if he proves to make a habit of it rather than it being one bad kill he can get in trouble for that.
Shooting of wood pigeon is not illegal, neither is shooting wood pigeon in your garden. But there are rules in place that make it legal. Firstly his rifle must be below 12ft lbs without a FAC licence. To shoot in your garden you can't be closer than 50 yards from a main highway, the pellet can't leave the shooters property. The shooting of pigeon is also legal as long as they are a threat, for example I grow veg and protect them with netting from wood pigeon but they still get through and kill my crop, so legally I can shoot them and eat them. But for me to shoot just because I am hungry is illegal and I could get prosecuted. I understand your concerns and perhaps Mr X should practice more to avoid a inhumane kill and also give his neighbours a heads up to keep the piece.
Some kids were shooting each other with a pelet gun in our local park.I spoke to a beat policeman who said to call police if ANY kind of gun was being used in a public place, he said they would atend straight away and would even put the helicopter up!
All wild birds are protected by law though some species may be controlled by lethal means through a licensing system operated by Natural England. Certain species, Wood Pigeons being one, currently appear on a general licence which is freely available to landowners or other authorised persons. General licences don't have to be applied for but can only be exercised in specific circumstances. The list of species appearing on all of the general licences is reviewed annually.
Wood pigeons are on this year's general licence permitting the killing or taking of certain ‘pest species’, or the destruction of their nests or eggs, by authorised persons for the purposes of preventing the spread of disease or serious damage to livestock, agriculture or fisheries interests; preserving air safety; conserving wild birds; and preserving public health and public safety.
It should be noted here that killing for the purpose of getting a cheap meal isn't covered by the general licence.
The problem as I see it is that with regard to the law he isn't (most of the time) committing an offence. As has been mentioned it is when the pellets leave his property that the offence occurs. I know it might be difficult but trying to collect or mark where you find any before you call the police might help.