I don't believe that stricter gun control can have a negative impact on gun crime. The stats you give for the UK are just not correct.

The UK has one of the lowest levels of gun ownership and one of the lowest rates of intentional gun deaths. The gun crime rate rose between 1997 and 2004 but has since slightly receded, while the number of murders from gun crime has largely remained static over the past decade.

A Home Office study published in 2007 reported that gun crime in England & Wales remains a relatively rare event.

In 2005/6 the police in England and Wales reported 50 gun homicides, a rate of 0.1 illegal gun deaths per 100,000 of population. Only 6.6% of homicides involved the use of a firearm.

By way of international comparison, in 2004 the police in the United States reported 9,326 gun homicides. The overall homicide rates per 100,000 (regardless of weapon type) reported by the United Nations for 1999 were 4.55 for the U.S. and 1.45 in England and Wales.