I've been clear that I don't consider the Brexit referendum to have been democratic. I stand by that opinion. But of course there are amounts of democracy. We have elections - democratic. We have a monarchy - not democratic. We have healthcare and education - democratic. We have restrictions on the size of the family - not democratic. We have freedom of expression - democratic. We have restrictions on protest - not democratic.
All of modern society operates as a balance between democracy and restrictions on that democracy. A 'true' democracy, a pure democracy as it were, would be anarchy.
While there is private education and healthcare, postcode lotteries, waiting lists...you pay more, you get better treatment... they are only only vaguely democratic, although I disagree with the term to describe them. The other things you mention are not restricted,or free, they just come with a cost...which some can afford and others cannot. None of these are democratic or otherwise unless you start confusing it with egalitarianism.
Even our elections are only partially democratic because of the restrictions on who can vote, and what they can vote on...decisions made by our governing classes.
Monarchy is not democratic and has never pretended to be, but there is no requirement for every aspect of life within a democracy to be democratic.