I've said it before, but it's kind of obvious, even at the time, that the Referendum wasn't called to decide whether we'd leave the EU or not, but to kill the question. As far as I can tell, most of the questions of what is or isn't democratic stem from the fact that the Referendum was launched in the first place in bad faith.
In a more sensible world, the Referendum would have been established from the get-go as merely the start of a process, ie something like:
1. a vote to decide whether or not we should trigger A50;
2. two years of negotiations (able to start instantly, because there would have been no question that the referendum gave the legal power to notify), where the party in power had already done or at least thought about the work necessary to leave;
3. A further referendum on the terms of withdrawal, or on whether to go ahead with leaving on those terms.
If this had been established from the start -- and, by the way, this is the sort of thing that David Davis had envisaged, so in a sense I'm writing a Leaver's manifesto, not a Remainer's -- then a second referendum would have been seen as Democratic. Sadly, all the Leavers who won then promptly seemed to forget their own visions for the process, and -- to be fair -- the Remainers who lost decided to hijack this otherwise sensible process for the same cynical reason they'd had the Referendum in the first place.