The issue was that support for "Brexit" was a bad-faith fabrication by Murdoch-owned media with a dash of foreign-funded interference.

When you put down any specific Brexit implementation and asked people to vote on it, you generally got supermajority opposition.

This is similar to, for example, the nitwits in Kentucky who fiercely opposed Obamacare but were vociferously supportive of Kynect and the ACA--all of which are the same thing.