The question was “in or out”. Britain (mostly England) chose “out”, because evidently they don’t teach history in the schools.
What the campaigners promised wasn’t linked to the reality of the EU treaties UK had signed when the EI formed, or the reality of needing to negotiate with the EU from a significantly weaker position.
Maybe another negotiating team would have gotten a sweeter deal, maybe not. In any case, it’s the deal UK voters asked for (by electing successively worse governments).