It's not the death penalty that's the deterrent. Nor, really, is it any jail sentence. It would appear that many people believe that they can kill and get away with it - that the police forces will never catch them.
But 92% of killings get solved. That's the most recent figure I've seen. And with the advances in DNA and other forensic sciences, more and more killers are going to get caught. maybe our police should make far more of their success in this crime, at least.
And, for an example of a dreadful miscarriage of justice that would, in less enlightened times, have led to an execution, look no further than the case of Stefan Kiszko. Found guilty of the murder of an 11-year old, perjured by witnesses, defended lamentably badly by a man who would become Home Secretary, he would have been hanged without a doubt. And he could not possibly have done it.
https://en.wikipedia.org/wiki/Murder_of_Lesley_Molseed
So no, I can't agree with a return to capital punishment. One wrong hanging offsets all the many that may have been justified.