Yes. That is called represantative democracy ffs.
And they can vote on a lot of things, but there's also a very high treshold for those referendums to actually succeed. As I said, please broaden your view beyond what The Sun has been telling you. It's not that hard. Ans by the way, the Swiss are rather dissatisfied atm because there's so much referendums in recent years it stalls political progress.
How is ignoring one half of your population, completely ignoring it, helping giving moral support to decisions? It doesn't and that is exactly what you are seeing right now in GB.
Your last sentence might be right, but that doesn't change the fact decisions like this shouldn't be put up in referendums.