Legally it was advisory. But it was an offer of contract, which was accepted and acted upon by the electorate, breach of which will lead to serious consequences if the imbeciles in Parliament thwart Brexit.
Furthermore, although the people have historically been satisfied that “Parliament decides” is an acceptable way of doing things, since the UK joined the various predecessor structures of the EU, that has not been the case and since Maastricht it has become increasingly bleeding obvious that membership is simply ultra vires since it is transferring decision making, not back to ‘we the people’ who own the inalienable right to govern ourselves, but to the unelected and unaccountable EU.
On that basis the legal status of the referendum is irrelevant.
The reason we have not had revolutions, and political turmoil as in Europe is because our common law constitution gave Parliament sufficient leeway to be pragmatic enough to avoid being overthrown.
If Parliament doesn’t work for us (and inside the EU it doesn’t) then WE will change it.