A number of factors effect that graph, some you would not be excepted to be aware of.
First the dates on the graph are chosen to show a specific picture, looking at a longer time frame we see a general upwards pattern that continues after the handgun ban. This turns for the first time in 50 years, 8 years after the ban.
Second a large part of the 2000 - 2002 peak comes from the actions of one man Harold Shipman who was a doctor who had been murdering his elderly patients with poor medicine for the last 30 years, he was uncovered in 2000 to 2002 and 250+ murders were attributed to him in that period though they had been committed before, not gun crime related at all.
http://en.wikipedia.org/wiki/Harold_Shipman
Thirdly is the fact that the UK has never been a high gun ownership culture, even pre 1996 guns for home defense were not common. The dunblane massacre just pushed a bit further down the road from a low gun culture to a very low gun culture, the 1996 act isn't what made the UK gun free its probably 150 years of different culture before that.
Finally I do think there was an elements of a genuine increased in murder rate in the late 90's, this is when crack cocaine and gang culture took hold in some of our larger cities.
Be careful when some who is receiving money Gun companies, produces a graph with a limited set of stats saying there is no link between people having guns and people getting shot, they might not be telling the whole truth.