I'm not certain, but I think that if the gun is not allowed under the limits of weapon types, then if they were found they could be prosecuted. Wikipedia[1] has a good breakdown of the types and restrictions.
Basically, if they had shotguns and hunting rifles which fall under the legal categories, then I think they'd be allowed as many as they want provided they pass all the requirements themselves - e.g. criminial record, mental history etc.
If they have illegal types - handguns, automatic weapons etc. then it's illegal, regardless of how long they've had them. When handguns were made illegal there was an amnesty but now posession would be illegal.
One thing to bear in mind as well, some people argue against banning guns by pointing out that criminals will still get guns. This is true in that it does happen, BUT with a much smaller number of guns it is a) harder for criminals to get guns, and b) much, MUCH easier to track them. Supposedly in London, a lot of crimes are perpetrated with the same guns, and these are much easier to track back to people and therefore much easier to get convictions.
[1] http://en.wikipedia.org/wiki/Gun_politics_in_the_United_King...