For what it’s worth, i wouldn’t shoot with the point of aim in the air, but it would depend on where it is. Out in the middle of no where, no problem. In middle of housing estate, probably not.
If you do go down that route, talk to the neighbours as air rifles can look like full on sniper rifles to the less informed.
You can pick up a SMK XS78 for around £99 including a scope if you shop around, but generally not available mail order. Its a very cheap rifle, runs on CO2 canisters and usually under powered out of the box at around 9 ft/lbs which should be more than enough for pigeons at 20 yards or so. Provided you aren’t shooting in massively varying temperatures, there are accurate and consistent.
Make sure the rifle is below the legal limit of 12 ft/lbs. Its the owners or users responsibility to make sure it complies, even if it has just been bought from a dealer and still in its box. As far as the law is concerned, i don’t believe there is any distinction between an rifle that is over the limit or a assault rifle. The other issue is that its a bit woolly as to how the police determine whether an air rifle is over the limit or not. For instance, i have a AA S400 that is set up with AA field pellets and maintains 11.5 consistently. With bisley mag pellets it will go up to 11.8 ft lbs. In a police check, they will use whatever pellet they can to get the highest reading, all they have to prove is that the rifle is capable of going over the legal limit. This is assuming the police check this at all, there is an ongoing incident with a competition match shooter that has had his rifles confiscated and facing prosecution as they are over the limit by .2 ftlb.
As for accuracy, i can get pellet on pellet at 35-40 yards and i’m no competition shooter. PCP rifles are very accurate with the right pellet. Springers are just as accurate, but need a bit more practice.
Re: hollowpoints: Fine if your range is less than 25 yard, but beyond that they can get unpredictable i find. They don’t really do much anyway, the pellets are subsonic so i don’t see them doing anything more than a diablo shaped pellet on a live target. Good for punching holes in paper targets though..