The Police in the UK do periodically hold firearms amnesties where anyone in possession of an unlicensed gun can take it in to a Police Station and hand it over without being arrested or asked for their names. I don't think there's ever been a buy-back but I think it sounds like a good idea.
Normally, the penalty for illegal possession of a firearm is very severe, 5 years for most crimes or 10 if the judge believes the reason for possession was related to national security or a possible act of terrorism. This seems to be enough to make carrying a gun unattractive to most low level criminals. Being an island helps too. It lowers the number of routes people could use to import illegal guns and makes being caught more likely.