UK citizens were never given a vote on their 'citizenship' rights in the EU.
UK citizens only voted to join the EEC - not the EU. They voted to join what was essentially a 'trade block'. Not a supra-federal state. (UK citizens were not given a vote on the treaty of Rome.)
The French voted against the treaty of Rome - and guess what? Their Parliament enacted it! How's that for consensus?
Same thing in the Netherlands.
In Ireland, they were forced to 'keep voting until it passed'.
Most other countries did not get a referendum on joining the EU.
There was never any 'popular consensus' on the EU as we know it - it likely may never have existed if it were put to referendum.
I would argue that a 'strong consensus' would be needed to have Scottish, Catalonian or Quebec separation - those are parts of nations.
The EU is not quite the same thing.