I didn't downvote but I found your point utterly specious. Meetings have quorum rules to prevent skulduggery, a minority group colluding to pack a low-attendance meeting and vote on momentous issues. A national referendum is open to anyone eligible who cares to vote.
Let's say, fantastically, only one person had turned out to vote in the Brexit referendum, and the whole thing were decided by one vote to nought. So long as the referendum had been free and fair, adequately publicised and properly counted, it would completely represent the will of the whole country. Elections are decided on the opinion of those who bother to come out and vote.
As for the regions and demographics, it's a decision for the whole United Kingdom. Are there actually any serious alternative ideas to giving one vote to each living adult person?
p.s. I voted Remain and agree with 'chucking it away so frivolously'. I just think trying to re-slice the sausage different ways based on subsets of the voting is pointless.