Dave, I don't know which side of the argument you are on but I very much doubt there is any connection between the rise in violent crime and the handgun ban. (However much I would like there to be!)
Firstly you must realize that in terms of % population, the numbers of handgun owners was tiny. I have been involved in shooting sports for about 50 years and I have never personally known anyone who has had a handgun other than for humane despatch of deer and then only two.
However the vast majority of people who did own handguns had them as collectors and target shooters, not for personal protection.
I believe that the only place that non-police or armed forces personnel were (relatively) commonly allowed to have a handgun for personal protection was in Northern Ireland, with very few exceptions.
To have used any weapon for personal defence would have always put you in a very dubious position legally. Many are the cases of people who have used there weapon for protection of person or property and have found themselves in the dock as a result.
One difficult truth for North Americans to comprehend about the UK is that we have never had a common 'gun culture'. Guns have always been owned by a small disparate minority who are viewed by the vast majority as strange and probably a little deranged!
This is why it has been relatively easy for us to get stuck with ever tightening firearm legislation: the general population don't get it and we are too few and fragmented to have a strong lobby to defend ourselves.
At a time in our history when North Americans were having to feed and protect themselves with a firearm, we were busy executing and transporting people for poaching a pheasant. At that time in the UK only the rich had the opportunity to shoot and the wherewithal to afford guns.
With the industrial revolution and sporting possibilities of the colonies came the interest in sporting shooting but still it was a pastime of the wealthy and privileged.
Around the turn of the C19th there was a degree of democratisation of shooting sports but it was a slow progress that was fatally damaged by the 1st WW.
The 50's and 60's saw the rise in clay pigeon shooting for the working man, especially as transport became more affordable, but it never grabbed the population as a whole.
And finally the atrocities of Hungerford and Dunblane, helped by an unsympathetic media, only confirmed what the general population had always believed...!
I truly wish that there was a connection between the handgun ban and rising violent crime which might result in the ban being lifted but there isn't and that argument is never going to fly in the UK.
If anybody was brave enough to suggest some sort of readily available 'concealed carry' permit in the UK, there would be a vast outcry from politicians, media and the general population.
And I have to say that I would agree.
What arguably works in one country just can't simply be applied to another. Take the NHS for example...but that is a whole other subject and even more OT!