In the UK I believe it has ... murder used to be headline news for days, today it often doesn't get a mention above the activities of some 'celebrity'.
Even the punishment for murder has become laughable, how many murderers have been released after 5, 8, 10 years some being free to walk the streets in the same location as the widow/children of the murdered person as a constant reminder of the injustice of 'the system'?
Well, I can point you in the direction of somebody who has spent nearly 40 years banged up for a murder committed when he was fourteen (and which he is completely penitent about, and always has been).
If you look at the matter of murder rates in more depth, you find the issue is far from straightforward. There are legal definitions to take account of, extenuating circumstances, detection rates and the impact of advances in forensic science, the dependability of juries (about which next-to-nothing is known), & so on.
As for whether the deterrent effect is real, it's questionable - after all why do they still feel it necessary to continue executing people in, for example, Texas? If the deterrent was real, well, I'm sure you can complete the rest for yourself.
In this country, anyone convicted of murder receives, as far as I know, a mandatory life sentence. There is a further component to the sentence, known as the "Tariff", which is the number of years that must be served before the "lifer" can be considered for parole.
Once released, a "lifer" can still be recalled to prison, and the reasons for this don't need to have anything to do with offending. It's not really the soft option the Daily Mail likes to call it.