I agree completely with you. Personally, the referendum in my opinion should have been "Remain in the EU" vs "Clear defined vision for what we want after leaving the EU", literally any of the definitions of it; "hard brexit", or "soft brexit". That would have killed the ambiguity, and would have ensured that any the end result of such a referendum would carry the support of all the people who voted to leave.

I don't think a yes/no vote on a complex issue where there was blatant propaganda (bordering on misinformation) in support of either side really tells you much about how citizens feel about the actual complexities of case.

Phrased differently: no. I do believe the UK is deeply split on whether to believe certain media/politicians though.