Re: "clear democratic majority"
The Conservatives won a majority in 2015 with a much lower percentage of the electorate - 24.3%. The 37.4% figure for the referendum is a lot higher than that, and in fact no government has polled a similar percentage since 1966.
If a quarter of the electorate is deemed a sufficient mandate to raise VAT, cut the top income tax rate, introduce the bedroom tax, etc etc, then a third voting to Leave has to mean we leave. Sadly.