So how come people are saying that even if the majority want it, it shouldn't be brought back in, but when the majority wants Brexit, which clearly is to the detriment of most working people here, they mustn't be over-ruled because it's undemocratic?
I think my post may have come across in this way, but for me, the issue is that the referendum has happened. I don't think it should have happened, but it did, and so it's difficult to ignore the result.
If - God forbid - some idiot decided that we should have a referendum on the death penalty, and the country voted in favour of bringing it back, I think it would be difficult to ignore that vote.
If you just want to assess public opinion, you could do an opinion poll, hold done focus groups or whatever. By holding a referendum, I think the government creates a reasonable expectation amongst the electorate that their democratic wishes will be respected. The vote cannot simply be disregarded.
Personally, I can't really think of any situations in which I would want important issues to be decided by a referendum, rather than by elected representatives in parliament. However, if you do go down the referendum route, I don't think you can just ignore it if the public chooses the wrong answer.
I sincerely hope that we never have a referendum about the death penalty. I sincerely wish that we had never had one about our membership of the EU.