I suppose it depends on how you define 'democracy'. What always seems to be ignored is that only a minority of voters voted to leave. The majority - a large majority at that - either voted to remain or didn't vote. I don't view that as a democratic decision.
You could use the same argument against the last General Election or any General Election for that matter, that's only statistics. The voting system in the UK, rightly or wrongly is the first past the post is the winner so if anyone changes it now then they should be aware of any future consequences
I don't agree it's 'only statistics'. It is a proven fact. But when you say "The voting system in the UK... is the first past the post is the winner" that's simply not true. It may be true for general election, but it certainly isn't true for WA elections, or Scottish Parliament elections. They both use a form of PR.
But the main point is that we do not govern by plebiscite. Our system of National government is through democratically elected MPs, and most of the MPs - except the extremely wealthy ones - see the value of remaining in the EU.
Voting in the Brexit referendum was dominated by older voters, while the young (who overwhelmingly voted to remain) will have to live with the consequences. The European Union has 502 million citizens. Just 109,964 Irish votes prevented them getting a better functioning, more democratically accountable EU. That was the winning margin for the “no” vote in the Lisbon Treaty referendum. National referendums on EU questions are fundamentally
undemocratic by allowing tiny minorities to dictate to the majority.
Meanwhile, the majority of voters (not statistics, merely fact) will have to live with the consequences of the minority believing the litany of lies and misinformation spread by the Leave brigade. If it weren't so serious it would make a great basis for a sitcom.