It's not a gun or no gun thing, it's entirely dependent on culture. In most traditional western style european and european descendant countries, crime as a whole is low amongst those ethnic groups. The problem is either rooted in poverty or in increased crime by minorities.
See: Switzerland, Idaho, Wyoming for proper examples of nearly all-european regions with gun freedom and Chicago, LA, and Nigeria for non-european regions with restricted gun control.
It is the America gun freedom at the core of Government, and in action with the people, combined with the current world trade, that is keeping people in other nations free.
If America were not a big nation in world trade and military, many gun control nations would take over their citizens, formally, and make real slavery... or slaughter many of their people. Hitler was the example that proves this out.
The only basic reason the Hitler thing is not happening in the UK and much of Europe right now is, they have to keep face with America for trade and other reasons.
So, it is gun freedom that is keeping the world as free as it is. The UK gets a free ride to freedom, based on the fact that there is a whole lot of gun freedom in America.