Normally the result would be overturned. See Lutfur Rahman:
https://www.bbc.co.uk/news/uk-england-london-45452342Apparently the Brexit referendum was "advisory" so this doesn't count.
> sounds like a failure of the government structure and charter
Everything is a failure of the government structure and charter at the moment, pal. We've had half a dozen constitutional crises this year and the Speaker is digging up precendent from 1604.