The problem is that it was an advisory vote

This is sometimes raised, but is misleading. The only reason it was legally advisory is because in the British system of government, the UK cannot bind Parliament; the House of Commons can override anything else.

In the system of government in some countries, the option for a meaningful legal difference between two types of referendum exists.

The British government had been explicit that what the British public voted for would be implemented; this is the closest analog to a binding referendum. Had they simply wanted to request the advice of the public, it would have been announced that they would take the outcome under consideration.

This is not to say that having that referendum was s good idea. It is just to say that the binding/advisory nature is really a property of the British system of government, not to indicate that the intent was to merely take the public's vote as advice.