Here's your English homicide rate. Homicides were falling before the 2006 gun act, but falling from a peak that had been climbing for some time.
www.ons.gov.uk/ons/rel/crime-stats/crime...recorded-as-homicide
Here's the US homicide rate, which has been falling since the 80's, after a spike, but following the long term trend.
thepublicintellectual.org/2011/05/02/a-crime-puzzle/
and here is the US gun homicide rate, which is about half of what is was ten years ago
www.nationalreview.com/corner/427758/car...ng-charles-c-w-cooke
The point being, that if fewer people are being killed, it is likely that fewer people are being killed with guns. In the absence of guns, people are still being killed. Guns themselves do not correlate to the killings, as the US has nearly twice as amount of guns in 2015 as it did in 2010, but the gun homicide rate is half of what it was. If there was corrlation, Switzerland, awash in guns by UK standards, would have a higher homicide rate than the UK, but it does not; in fact it is one of the safest countries in the world, despite the guns.
Our problem in the US centers on illegal handguns in the hand of urban gangs fighting over drugs. The guns they have are illegally purchased, with drug money. Any restrictions imposed do little to change that fact. Alll the most restictive gun laws in NY, Chicago and DC have done is to demonstarte supply and demand, and drive up the price of guns, wwhich makes it lucrative to smuggle them in, and forces crimianls to steal more to pay for them, unintentionally driving up property crime and robberies. The unlawful criminals will not "turn them in" in a UK or Australian style program, and the average US gunowner is more likely to react to such a program by forming militias, Lexington and Concord style. I note the low participation arte in Connecticut over their assault weapon and high capacity magazine ban. Apparenlty all the gun owners in that state lost theirs before the turn in period, all at once.
There are things we should do to lower the homicide rate, but they cost money, and I mean dump truck loads of it. Reduce poverty by enforcing education. Tie entitlement programs to educational progress and work. Rehab habitutal felons (note that in the US, that studies show 90% of murder victims have criminal records themselves). Force gun stores to increase security, as most gusn sold in cities with restrictive gun laws are stolen from rural gun shops by smash and grab gangs that specialize in the illegal gun trade. Bulldoze ghettos in St Louis, Baltimore, Detroit, New Orleans, Camden, LA and Chicago and replace the blight with modern subsidized housing that instills pride and increases safety, where the dwelling are monitored and any excesive damage forces an eviction notice. None of this is popular for politicians who depend on votes to keep a job, but it's what we need.
As to gun ownership and gun crimes, I would point out that governments, including many of the ones poeple compare the current US homicide rate to, have killed more people in the last 100 years than criminals have, by a factor of thousands. Porgroms, holocausts, invasions, genocides, colonialization, death camps, these are things governments have done, and are still doing, to those they find that can't resist. My one rifle may not be able to prevent tyranny on its own, but my 100 million neighbors aremed with their rifles collectively guarantees that no government, foreign or domestic, will take my rights without due process.