I did consider buying an air rifle for squirrel control, but its a moral dilemma. The bonus if I could bring myself to become a serial killer is our wood is also full of pheasants and pigeons, which is free meat. Even if I could shoot one, there's still the issue of skinning and gutting, so Tufty and friends are looking pretty safe at the moment.
What surprised me is how accurate, silent, effective and expensive modern air rifles are. If you want to shoot loose wild targets humanely (eg squirrels etc) you really need a good quality accurate rifle rather than some budget brand. A decent Weihrauch, Air Arms or BSA Pre-charged are amazingly accurate, you should be able to group within 2-3 mm at 40yards, many of the shots going through the same hole- so if the quarry stands still for a second, a head shot is fairly easy for a competant marksman. But you'll need a budget of maybe £600-£1000, as theres not just the rifle but £200 for your bottle or pump, the scope, bag, silencer, and spare magazines to be considered. A shotgun can be a lot cheaper than a top of the range air rifle, but then you need the licence.
If alternatively you just want to despatch squirrels as effectively and affordably as possible rather than seeing it as a challenging 'sport', your best option is to live trap and then see them off with a more affordable rifle from close range, which could be a spring rifle for maybe £100-£300, or use a lethal trap.
Rural types like farmers seem to have far less problem than soft townies shooting pests and killing, when you farm and live in the countryside you experience livestock being sold to slaughter, pests being shot and the cycle of life and death on a daily basis, so they have to be far harder.
That said, my farmer pal Rex is one of the softest farmers anyone has ever known. His wife realised some of their chickens were geriatrics which is why they'd stopped laying, so she asked him to snap the neck of a couple. He had nightmares about it, took a sleeping pill, got up in the night half asleep and fell out of the upstairs window, rolling down the thatched roof before landing with a thud in the garden (unhurt). When he finally summoned up enough courage to have a go at a chicken, he aimed a 12 bore at one from point blank range, faced away and pulled the trigger. The result was he covered the farmhouse in feathers and chicken pate.