Not necessarily, according to recent reports showing that violent crime is still a big problem in the UK. Criminals are simply finding other ways to create bloodshed and terrorize the citizenry- knives. This is a perfect example of why gun bans don't work.
The UK is often used by the anti-gun crowd as an example of a modern, peaceful, safe utopia because of its very strict gun laws. The British Bobbies (police) aren't even allowed to carry firearms, although some special units are allowed to have them, and they are carried in some of the police vehicles, accessible only in emergencies and with a supervisors permission (as if that's going to help an unarmed officer who is about to be shot by a suspect- "excuse me Mr. Gunmen, could you please hold that position while I check with my Supervisor to get permission to obtain a gun, so that I can kill you"?). But the revelation about knife attacks shows that the UK is nowhere near the utopia that the anti-gun folks would have you believe.
What the reports show is that the gun laws in the UK have only created a nation full of sitting ducks, vulnerable to violent thugs (the same environment that thug sympathizers and anti-gun advocates want to create here in the U.S.). The laws have done little to prevent violent crime. People can't even feel safe in their own homes.