Well, there was sort of a second, but that could best be described as Remain.

https://en.wikipedia.org/wiki/1975_United_Kingdom_European_Communities_membership_referendum

Looking at approval polls in Eurobarometer, as I recall, British opinion on the EU tended to trend downwards after the Maastricht Treaty. So the public was kinda onboard with a looser organization, but not as much with a tighter.

Also, the referendum happened to rather unfortunately coincide with the European migrant crisis, so you had upset at immigration hitting a fever pitch right about the time the referendum was run, and some of the campaigning related to it (like taking back control of borders).