Actually that's what it would be if there was no constitution, though it would go by a different name.

The UK is a constitutional monarchy with democratic elements, it's not a democracy. That's why the people are Her Majesty's subjects, they're not citizens. As a consequence the people don't give orders in an absolute sense as they would in a CH-style democracy, hence it may be that parliament can't make a referendum binding before the fact even it wanted to.