It is estimated that there are fewer then 1000 illegal firearms in Britain.
It's not a direct simple relationship between illegal firearms trade and lax gun regulations but very strict regulations will cause the trade to dry up.
That's not strictly true - he estimated that most gun crime in Britain can be traced back to 1000 or so illegal firearms. That's quite an understandable statistic considering how guns get passed around in the underworld among gangs etc, that will involve a lot of re-use.
He didn't say that was an estimation for how many illegal firearms there are in Britain in total. The reason why I'm making a point about that is that in Northern Ireland you could potentially find enormous dumps of illegal firearms - submachine guns, AR15s, AK47s, but mostly handguns. The police find them all the time. The thing is though they aren't actually used in any kind of gun crime - they're just being kept around by paramilitaries "just in case". Similarly, there will be a lot of guns on the British gun market that are not used in gun crime; they're either getting bought and sold, maybe even passed on to other countries like Ireland, or they're being kept in caches for future use. Only one or two guns out of a cache of perhaps 20 will actually end up being used in gun crime. I know the IRA tend to keep their arms caches in the South so they can be used in crime in places like Dublin, but the UDA and UVF have similar arms caches in the North and it can be difficult to transfer guns across the border for future attacks so it makes sense the various paramilitaries will try to keep caches at least somewhere in their areas of influence.
I'm wondering though if, rather than the strict regulations actually causing the trade to dry up, the fact that Britain is so far-removed from any kind of serious conflict zone or similar where there's a lot of illegal firearms floating about naturally has more to do with it. I know Northern Ireland was pretty explosive in its own way, considering the vast quantities of illegal firearms that ended up in the North following that, but we've had very comprehensive arms decomissioning/surrendering programs over there that have taken a lot of the stock off the market. We know the IRA had roughly 1,000 rifles back in the 1980s, so that would be in addition to whatever was being used in Britain. It's quite interesting that even during an insurgency, when semi automatic rifles were legal, the IRA only had 1,000 rifles to their name. Somehow I think we can discount that statistic for the same reason that the police like to give very reduced estimates of protestors at political events. I also notice the statistics the BBC quoted when it gave that figure didn't make a mention of any SMGs, of which the IRA seemed to have hundreds.
Slovakia on the other hand is right on the doorstep of the former USSR - after the USSR collapsed, it's not like there was a war that caused all those ex-Soviet weapons to get spread around everywhere. The underworld just got its hands on them in the economic chaos in the '90s - those guns are still around now, arguably far more of them on the European continent than on the island of Great Britain or in Ireland. In addition to that you've got Chechnya and all sorts of areas of instability that contributed to the continental arms trade. The fact that we're spread over two islands probably has something to do with it too - it means illegal arms traders/suppliers need to find other ways of transporting the guns into the country, such as by boat, whereas Slovakia has all kinds of borders.