I'm sure that, as demographics and society change over time, the UK and other countries will have increasing issues with violence. There are always those who will disregard gun laws and acquire illegal weapons, whether for planned criminal activities, internal disputes among immigrants or just to make money selling them.
Even if there IS some increase, the strict laws and fewer guns will keep the UK relatively much safer & saner than what we must deal with in the US.

Sadly, I can't see any easy way for us to get out of this situation-- there are simply too many guns already in private hands.