A lot of people seem to think that the death penalty simply requires an auto-injector and some rat poison. Factor in the administrative costs, construction of a dedicated facility, the staffing, all the requisite testing of equipment and chemicals, legal proceedings and appeals, the inevitable EU Court of Human Rights intervention... then when the first execution happens, the cost of policing the inevitable protests and demonstrations...
I'd rather see the those that can't be reformed left to stew in a prison cell than having a quick death. Imprisonment (to me) is a symbol of defeat, whereas execution; death is freedom, a release.
As for the Lee Rigby murderers, would executing them cause them to be exalted as martyrs by some religious extremists?