What he says is mainly ok, but it was irrelevant how many voted in the UK general elections because one has a right to not vote. Plus we know the upper house could be better; it needs to be fully elected, preferably without political parties, and with only a portion up for re-election at a time to avoid emotional swings. And change to the Lords has been proposed, whereas there is next to no chance of proposing something similar for the EU.
Of course civil servants have influence with any government, but someone has to enact parliament's decisions, and keep the day to day stuff running smoothly.
Granted the parliamentary system could do with a complete overhaul too, get rid of parties in the Commons would be a start; ensure elected members do gather the majority view of their constituents and represent them accurately; but there is no realistic way that will occur any time soon anyway. And it's still far far better than the EU system where you only get to vote for those debating whether to accept the new laws or not yet. At least when one's own country is in control of itself there is a fighting chance of improvement.
As for the rest, for sure no one knows for sure the result details, which is why the fear stories of what might happen, no matter how ludicrous, are spread around. But any change brings challenges and opportunities, and in the medium term they all settle down to the new status quo.