I live in the US and part of my job is campaigning for an end to the death penalty.
There are so many reasons why going back to the death penalty would be a mistake in Britain:
-innocence. Here in the US there are now more than 150 people who've been freed from death row because they have now been proven not to have committed the crime which the court was so sure they had
-cost. Death eligible trials would be very expensive on both the prosecution and defence sides and death sentences would mean years of costly appeals. Life without parole is actually cheaper, contrary to many people's assumptions. In a modern society, you could not cut the appeals and thoroughness of the trial as you once could because the human rights-based challenges to that would be huge.
-arbitrariness. The death penalty is absolutely not given to only the worst of the worst by some sort of "scientific" determination of who the worst criminals are. In fact race/national origin of defendant and victim, location and other extraneous factors are likely to play a part in sentencing decisions
-harm to victims' families. Prosecutors here may try to persuade victims' families that the death of the defendant will bring "closure". It's a mirage. Sadly - and I know many murder victims' family members - the only answer is time and reconciliation. Life is always going to be different after you lose a loved one and another person's death really really won't make it better. There are so many stories of families who thought it would all go away once the defendant died. It didn't. Also, families have to relive the nightmare every time a court hearing happens for an appeal. There's no chance to move on
-there's evidence juries won't convict despite a belief a defendant is guilty because they don't want him (it nearly always is him) to be killed
-the deterrent effect of the death penalty is highly questionable. Lots of evidence that people underestimate their chances of getting caught or don't care in the first place (mentally ill, intellectually disabled, blind rage, substance abuse and addiction)
Another philosophical point: if death is the right punishment for murder, presumably you also think rapists should be raped? And if not, why not? And who will carry it out and what will that do to them?
The death penalty is barbaric. Someone who works with death row prisoners and acts as their spiritual advisor said to me, "I know as soon as someone tells me they support the death penalty they know absolutely nothing about it. Because you only have to look into it for 2 minutes to learn enough to convince you what a terrible idea it is."
I could go on for hours!