Yeah nah. We have pretty much exactly the same Westminster system here in Australia, and referenda are by convention a binding element of that system.
A constitutional question is referred to the people when Parliament chooses to do so and then Parliament follows the decision. They don't get to go "hey Britain, whaddayathink?" and then refuse the answer "haha you utter twits, we're not doing that!".
You can make a case to say that's not written down anywhere but very little of the British constitution is. The proof of this pudding is every single one held in the UK has been honoured by Parliament.