The average British person has no idea how the EU works. They don't know what the different bodies are. They don't know who their representative(s) are. They don't know how to make their voices heard. Maybe a third of people vote in the elections, and they don't really know what they're voting for.
What kind of democracy is that?
How many Brits know that bishops sit in the house of Lords? Some know, sure, but many? How many of us know what the Privy Council is and who the members are? What powers are purely ceremonial and which have teeth? Why can't MPs resign like normal people? How and why there is judicial independence from parliament seems to be news to the Secretary of State for Justice, if she doesn't know how it works what hope do the general population have? Even how laws are passed seems to surprise people — "The Lords might disagree with us? Abolish them!" — to say nothing of the difference between primary and secondary legislation.
The UK has a constitution, but it's not written down in one place for convenience and understanding, it's spread over time-worn ritual, over the Queen's Speech and slamming doors in the face of Black Rod.
I mean, I keep reading stories about how famous corporations have terrible codebases which they can't fully fix it, and we're in a domain where deployment is trivial amd doesn't literally cost the time of the entire legal profession to familiaise themselves with the changes.
I'd love to be wrong. The saying "ignorance of the law is not an excuse" is necessary, yet at the same time not possible when the law is as complex as it is now.
The ignorance of the average British person about the actual functioning of the EU is indeed a problem, and probably a major contributor to Brexit, but that seems more of a failing of British education and media rather than the EU itself.
A poorly educated one. But still a democracy.