"The referendum result was not legally binding due to the concept of Parliamentary sovereignty. However, it was widely accepted that the vote would be the final say on the matter. In a 1975 pamphlet, then Prime Minister Harold Wilson said: "[. . .] I ask you to use your vote. For it is your vote that will now decide. The Government will accept your verdict." The pamphlet also said: "Now the time has come for you to decide. The Government will accept your decision - whichever way it goes." "
If the 2016 vote to leave is worthless, then so was the 1975 vote to remain. The real constitutional crisis was inherent in making the abdication of national sovereignty merely a (heavily downplayed) plank in party politics.
Three other countries had a referendum on the issue beforehand, in 1972 - and Norway said no. The UK waited for 3 years and held a referendum only because the Labour Party opposed EEC membership while in opposition.
Either we are headed out, or we were never in.