In all fairness Britain are the only self-proclaimed Democracy ("Oldest in the World", they tell us) with an even more undemocratic political system than the US, because in addition to a First Past The Post voting system, they also have a monarch with - as was exposed a couple of years ago - real power as head of state, an unelected Second Chamber with inherited and nominated-for-live positions and, probably worse, no written Constituition so any party in Parliament with a simple 50% + 1 majority can pretty much do whatever they want.
The FTPT + No Constitution combination is probably the worst part, as it means that a party with a mere 41% of votes of cast (so about the votes of only 1/4 of voters, due to abstention) - such as the current ones - can get a parliamentary majority (so, more than 50% of seats) and do things that in other countries would require constitutional changes (which generally require 66% or 75% of votes, depending on country), so things like changing the local definition of Human Rights.
Mind you, the Brexit vote isn't at all affected by these things, so your point still stands unaffected by those considerations.