I think most in favour of the death penalty would certainly apply it to those convicted of acts of terror. What is more heinous than deliberately targeting civilians? Take the Birmingham pub bombings which killed 21 people, the second most deadly terrorist act in Britain in recent times. Surely those six men convicted of the bombings should die for their actions?
Except those men were entirely innocent. The problem with the British justice system is it is littered with false convictions and miscarriages of justice, be it through incompetence or police corruption. That you would end up executing an innocent person is, to me, the most powerful argument against the death penalty.