The distance you have to worry about is 50m from the centre of a carriageway but you can ignore this iirc, if it does not cause distress to other people. Having said that you are allowed to discharge an air weapon (non FAC) within your garden but you have a statutory obligation to ensure the pellet does not leave your land.
Squirrels have exceedingly tough skulls and pellets (.177, .20 and .22) will sometimes just bounce off them (even guns up to the legal max). The best way of despatching a squirrel is through the chest (under the foreleg passing through the heart etc is best). If you haven't shot animals before don't be surprised if they run about, jump up and down, twitch etc when you have shot them it is just their system shutting down. To be fair to the squirrels though, you do need to be able to take them out cleanly. That usually means being able to shoot to a standard where you can put several pellets through a kill zone maybe the size of a 10p piece (for a squirrel) before you even try and shoot it. Then you have to be prepared to mess it up because of nerves when it comes to taking the shot… many people lose concentration and fluff it, either missing the quarry or wounding the animal which is unacceptable if it could have been avoided.
It isn't just a case of borrowing a gun. Oh yes, and beware ricochets and grumpy neighbours.