A referendum on the reintroduction of the death penalty, anyone.

The UK's dilemma over the implementation of the referendum result, to leave the EU, raises questions about the relevance of so called 'people's votes', especially when the Country is divided equally.
We might get an idea from the reluctance of every government since the mid twentieth century to hold a referendum on the re-establishment of the death penalty for certain crimes. All polls suggest that the reintroduction of the death penalty for some crimes such as the murder of policemen and women in the course of their duty would be popular in the Country and for this reason, parliamentarians are unlikely to vote on a referendum. But why?
Are politicians more enlightened than the plebs they represent? Have they a different sense of justice to the ordinary man and woman in the street? Or could it be that Parliament is full of legal officers that don't wish to burden their fellow judges with life or death decisions? Surely it can't be due to lack of executioners!
Failure to hold such a referendum is due to the cowardice of Parliament, afraid they couldn't, in conscience, uphold the will of the people. So much for democracy, a notion at risk as we witness various self interests contort the realities of Brexit.