I’m doing this one without links first, since I see no valid reason not to say what needs saying.
To propose, as has been done, the removal of all treaty obligations which prevent the death penalty forgets the origin of the removal.
The 1951 Homicide Act removed the death penalty*, substituting life imprisonment for those crimes (except High Treason and a couple of other offences) which still had the death penalty. This debate of removal had taken place over more than a century; from J.S.Mill onwards. This was done prior to any Treaty requiring the death penalty to be removed.
Protocol 13 of the ECHR, stopping the death penalty was introduced and ratified by the UK in 2003; we’d already removed the death penalty from any remaining crimes in preparation for this. the ICCPR Optional Protocol 2 also abolishes the death penalty, and we’ve also ratified that, although it does not have any domestic effect – our courts don’t have to follow the ICCPR.
So we removed the death penalty over a century or so, piece by piece before any Treaty required us to. It can be said therefore that the common law states that the death penalty is an anathema to the law – no sitting judge has ever wanted to use it in place of the sentencing options they had available.
It’s also worth considering the counter-effects of sentencing options on findings of guilt. Despite rose-tinted spectacles there were not fewer murders in the past, and although a murder could (if hanged) only kill once (or in a sequence) before being stopped, there were many murders that were not solved, or when taken to court, the accused were found not guilty because… What little evidence there is on Jury behaviour proves that they are reluctant to convict for serious crimes, and the more serious the punishment the higher the unlikelihood of a conviction becomes. So the death penalty would lead to a higher rate of non-conviction than the life sentence already does.
I would also like to add that I find it superbly irrational for a libertarian arguing the State cannot be trusted with taxes or health care to argue that the State can be trusted with the power of life or death over any person. Come back when your argument has fewer holes than the average seine net.
*Amend: the wording seems to suggest this single Act removed the Death Penalty – it was merely part of the Consolidating exercise on defences; but a step that was required in order for the Life tariff sentences to work in practice. A wording short-cut that says more than it ought.