There has been a general downward trend in police recorded homicides over recent years. If the provisional figure of 642 homicides is confirmed when the final figures from the Homicide Index are published, then this would represent a fall of 19 per cent in homicides since 2001/02."
and
"The BCS shows that the number of violent incidents increased gradually through the 1980s and then increased sharply after 1991 to reach a peak in the mid 1990s. The number of incidents then showed steep decreases in the late 1990s. Since then, despite non-statistically significant year-on-year changes, there has been an overall decline."*
The decline in violence is actually somewhat global and not really anything to do with firearms either way. What the gun ban does unambiguously reduce is the opportunity for mass shootings.
(Did you mean compare rates within the same country, or rates between the UK and US? The UK's overall murder rate is comparable to that of two or three US cities. Sadly this PDF only goes back to 2000/2001 and doesn't cover the 90s.)