Murder rate has always been lower than the US even when British citizens had equal access to firearms.
Americans have always had a propensity for killing.
Banning guns didn't lower the British homicide rate.
Relaxing guns laws didn't raise the US homicide rate.
Actually the difference between the two rates is falling (US is slowly getting closer to UK) despite UK banning guns and US relaxing gun restrictions.

Slightly long rant but here goes:
I blame mental health system and a systemic breakdown of family (children being raised in bad foster homes and group homes). Anyone reading up of attachment disorders can see that a human who doesn't bond with other humans can be very dangerous later in life. The lack of empathy means they simply don't care. They don't care about killing. That combined with no hope, no future, no chance to break cycle of poverty & violence creates a bad combination.
However solving the real reason for homicides in the United States is tough. It will requires billions of dollars and a generation (or maybe two). It will require consistent support from the government to help poor & struggling families. It will require support/treatment for drug abusers, and a functional child welfare system.
Blaming it on guns is easier.