Rod.
An air rifle can be bought over the counter (sub 12ft/lb's ) by anyone over the age of 18,they are not currently subject to any licensing requirements in England,Scotland however have now put them on licenses.
You can legally shoot your rifle anywhere you own as long as the pellet does not leave your property,you must ensure a safe backstop and reallistically a decent funnel shaped pellet trap.Plinking tin cans etc again is fine as long as the pellets don't stray.
You can also shoot on land not owned by you with the landowners permission.
In reality you have to be extra mindful of any neighbours,anything that is gun related is likely to cause hysteria and prompt a call to the police,so common sense needs to be applied if you are overlooked in any way.
I am lucky that I have a small piece of land (the size of a tennis court) behind our house and garden that is totally fenced in and only overlooked by one neighbour who has never made a fuss.My backstop is a handily placed brick built former Victorian pig sty at the far end of the 'range' so I am shooting into a totally enclosed backstop,it is perfect for air rifle shooting especially with a moderated virtually silent PCP rifle.The pellet hitting the target is the loudest noise and That is deadend to a soft thud as I pack the target holder with old bath towels.I do not shoot my unmoderated Spring rifles here as they just make too much of a crack and I don't want to upset the natives

I know it seems like a lot of trouble to go to but my home range is the envy of a lot of my shooting friends,shame it's only 27 yards.
I am also very lucky that the gun shop I tend to buy most of my gear and rifles from have just opened a superb airgun range,targets out to 60 yards,all undercover,purpose built benches and target holders,a full HFT course with dozens of knock down targets,plus a soon to be opened dedicated pistol and archery range,all this only 20 minutes from my door,and I have a full dedicated Hunter Field Target Club in the village where I live,less than a mile away,I can literally walk there.
Airgun sports are one of the fastest growing shooting hobbies in the England,access to the guns and places to shoot is much easier than full bore and even shotgun sports.Add to that we have some of the world's finest airgun manufacturers here and you can see why.