It wasn't advisory other than in a technical legal sense. The UK has no constitutional mechanism for binding referendums. Parliament could always ignore the public, because Parliament can do anything. Cameron just says "what you vote for is what we're gonna do", and you take that at face value.

If they'd wanted the analog of an advisory referendum, Cameron would have said "we will take this as input" or something like that.

I'll also add that, as someone in California, which places a larger-than-typical emphasis on (binding) referendums than most US states, I'd say that a large chunk of the absolute worst policies that I've seen have come from referendums.

That's not to say that I'd oppose their use in all cases, and given that Brexit was probably most analogous to an independence referendum, which is one of the few places where I do agree with referendums, it probably made sense.

But I would not favor expanding their use. The fundamental issue with direct democracy is that it's a lot less-costly to get a hundred or couple hundred people to really seriously look at and understand an issue to make an informed decision than it is tens of millions. A legislature is, I think, generally a better mechanism to use.

The only problem with that is the conservative party that took over wanted Brexit that to happen, so they were never going to pull that chute fir everyone else. They were just going to wait out the consequences on their piles of money.