Prime Minister Cameron would not have resigned if the referendum was simply advisory.
In theory, Parliament can set aside the vote of 17 million people to leave but as a practical matter, it would destroy faith in the country’s institutions.
To take the UK out of EU, Parliament needs to repeal the 1972 European Communities Act. It can deal with the rest after Article 50 is triggered.
Its not going to a clean and fast divorce. Its going to happen all the same over the next several years.
Legally the referendum was advisory. Practically, in terms of the UNWRITTEN British constitution, aka long-standing practice and custom, it was mandatory on Parliament, and the only issue is when the EU treaty two-year exit period clause is invoked. Britain is not America. Legal quibbles mean a lot less there unless criminal prosecution is involved.