It's true that violent crime in Britain (and, indeed, across most affluent countries) rose sharply at the time you say, but it was already on a steep upward arc from the end of WW2, until it started to go down dramatically sometime around 1990. I'm not sure the abolition of the death penalty has anything to with this. Indeed, social analysts are still at a loss to describe how the seemingly unstoppable increase of violence in western societies fell into a fairly spectacular decline in this period. Commentators in the USA have cited the "Wade vs Roe" case, which delivered abortion rights, as a cause. Others note that the rise and fall in violence are in a very close correlation with when western countries used, and then banned, lead in petrol; however, despite the close correlation, cause has yet to be definitively established. A further possible cause, more local to Britain, is the rise of ecsatasy and the dance culture, which certailnly contributed to the decline of football hooliganism.