If the death penalty "worked" (it doesn't) then no one would ever murder anyone else. (Although I leave this space here > < for someone to try and pretend they have some statistical insight that shows no one was ever murdered in Britain before 1965 when we did have the death penalty).
When you agree it's no deterrent that wanting to see it enacted isn't about some regretful necessity, but a rather more unpleasant venom soaked triumph of humankinds baser instincts.
There is also a staggeringly naive bordering on thick delusion that the UK legal system is somehow perfect and free from bias. A totally hypocritical delusion where people who in any other thread would have (or have been) whining about "two tier justice" are able to forget that for a minute in their supposedly fashionable bloodlust.
We should already be well aware of how the justice system treats people depending on race and social status. Why in the name of all that is holy would someone who claims to be interested in justice (spoiler alert, no one who wants to kill prisoners is, they're all about the rope) want to add capital punishment to that mix.
If people are so desperate to see people killed, then they are always free to emigrate to Saudi Arabia (or similar) where if they are really lucky they can get a front row at a beheading and be the last thing the condemned see before their head departs their body. But don't worry - they do put down large plastic sheets to avoid a mess.