It’s a question of form, generally referendums work by getting the people to accept a text instead of the Parliament. People can argue on what the consequences of the text will be, but not what’s in it. In the UK they voted on an abstract question.

So you think people shouldn't have a say on whether the minimum wage should be raised or on whether gays should be able to marry. Because, obviously, whatever the elite chooses is going to be okay for you, right?

Who are the "elite"?

I'm guessing they're not the elected representatives of the people, right? Otherwise, there wouldn't be a problem with them making the decisions they've been elected to make.

The people get a say by voting at general elections for parties that present a broad balance of deeply considered positions that reflect their views. This is why we have parties in Parliament and not just a giant bundle of one-issue politicians.

People felt strongly enough about progressive politics and the policies that went with that to vote Labour numerous times in the 90s and 2000s.

Anyone who felt so strongly about throwing the country into a tailspin by exiting the EU could have quite easily voted for the UK Independence Party in at least 2 general elections.

People's rights shouldn't be up for vote.

That sounds good but is ultimately an empty statement. Which rights are valid in the first place must be decided by vote.