No, it hasn't. In fact, it's gone down.
Numerous sources show otherwise and cite crime rates, including gun crimes, to be increasing since...
Ministers will also be concerned that the country is becoming increasingly violent in nature, with gun crime rising 23% to 6,375 offences
The ONS said overall crime recorded by the police rose by six per cent in the year to September, including a 27 per cent jump in violence against the person. It amounted to an extra 185,666 violent offences, bringing the annual total to more than 885,000 in England and Wales.
London's homicide rate overtakes NYC
This chart also shows that the gun ban made no difference as homicides remained at the same level and actually exceeded pre 96 levels a few times
See page 17
This shows that homicides actually went up after the gun ban only to return to roughly the same levels anyway...
Also - bbc.com/news/uk-england-london-39578500 Gun crime in London increases by 42% (2017)
If banning guns, as UK did in 1996 really was supposed to reduce gun crime than no year after 1996 should have more gun crimes than that year. Yet that is not the case.
"To say it has fallen is smoke and mirrors. Frontline officers are under increasing pressure and dealing with larger caseloads than ever before. This worrying rise in crime will only add to this pressure." - UK cop general secretary