Firearm-related death rate per 100,000 population per year...
Removing easy access to weapons and increasing police presence are two different aspects that affect the outcome of this. Also, focusing on the implement used in violence does not address underlying causes. Perhaps better comparisons might be homicide rate, number of law enforcement officials and average income.
US - 4.7 UK - 1.0 Afghanistan 6.5
Law enforcement/100,00 (2012/2009)
US - 248 UK - 307 Afghanistan 401
Average Wage ($US 2012)
Gross US - 55,047 UK - 44,222 Afghanistan 70/426 (2004/2010)
Disposable US - 38,753 UK - 29,938
Still a bit simplistic, but a shot (pardon the pun) in the right direction. It's not a simple interaction between one or two factors.