There are two classes of gun ownership in the UK.
Section 2 firearms are shotguns with a barrel no shorter than 24" and if magazine fed capable of holding no more than 3 shots.
Section 1 is basically everything else with a few minor exceptions not really worth bothering about.
For a S1 liscence you need to demonstrate 'good reason' for owning one. So, hunting, pest control, target shooting etc. Self defense is not a good reason. You also need to demonstrate that you have somewhere to use them. The amount of ammunition you can hold is controlled and is agreed at the time of liscence application. Records are kept and police have to be informed of every transaction involving a firearm. (Sale, Transfer or loan). Ammunition has to be stored under a separate lock to your guns. The number and calibre of rifle are specified on your licence, so you can't just go out and buy 20.
Section 2 is a little less controlled. You don't have to give good reason, but the police will expect you to have a clear idea of what you want to use them for. Again, self defense isn't allowed. Once you have your ticket you can own as many as you like. Police still need to be informed of all transactions (unless a loan to another liscence holder is under 72 hours). The only limits on ammunition are to explosives storage regs. That's about 10,000 cartridges.
For both S1 and S2 you need to submit a form, be interviewed by the police and agree to let the police have access to your medical records. A marker is placed on your medical records so if there are problems in future your Dr can inform the police. The police will review the security of your guns to ensure they are secure and no one else other than the licence holder has access.
Sentencing guidelines for firearms offenses which includes breaking any of the above, specify a custodial sentence of a minimum 5 years
Both licenses last 5 years. At which point you go through all that again.
It's a few hoops, but not as difficult or restrictive as it sounds. Unsuprisingly UK gun owners tend to be very sober and responsible individuals. Any infraction, even if it never gets to court will probably end up with your ticket being revoked which you may or may not get back.
In the US my BiL gripes about a 3 day cooling period for a hand gun. Rifles and shotguns are over the counter items......