I think the two most usual grounds for opposition to the death penalty, AOG, are:
1.That a civilised society should not sanction murder by the State, no matter how heinous the crime.
2.Miscarriages of justice cannot be rectified.
I think the first is a matter of philosophy. You either agree that some crimes are so despicable that nothing short of the perpetrator forfeiting their right to live will suffice, or you do not.
There are considerable difficulties with the second as there certainly have been some instances where a person has been wrongly convicted of a Capital offence. However, these are not as numerous as opponents would have you believe (though I accept that just one is one too many). But the often quoted cases of Derek Bentley (despite his conviction being quashed in 1998) and Ruth Ellis do not fall into this category, in my opinion.
I have two issues with the current arrangements:
Firstly the public (not unusually) were misled by politicians when the death penalty was abolished in the 1960s. They were led to believe that instead of facing execution those convicted of murder would spend “life” behind bars. No alternative interpretation of the term “Life” was provided to that then understood (i.e. the rest of one's life) and certainly not one so wide as in used now, where someone convicted to a “Life” sentence spends as little as eight years inside. Yes, I know they are released “on licence”, but that does not entail the sort of incarceration the public expects.
Secondly and again not unusually this is no longer a matter for the UK Parliament. The Council of Europe requires that all EU member states (and prospective member states) do not operate the death penalty and since there is more chance of me winning a Gold Medal at the 2012 Olympics than of the UK leaving the EU, that is that.