the obvious but still kind of interesting answer is that this is the outcome of a (globally speaking) moderately(ish) well functioning democratic system. This is broadly what people have voted for. You can say that it's a minority of people who actually vote for the tories, which is true, but with some fairly rare exceptions both parties for at thirty years have been triangulating and selecting candidates, making policy, doing communications based on what they think the electorate will like. They also have research systems which are pretty effective ways of hearing what the electorate want, I think. So what we get is a reflection of the desires of the british people en masse, not a perfect one obviously, but the politicians we get and the policies they choose, and how they decide to present themselves, is something that ultimately does come from the weird quirks of british people I think.
You reckon it's that one way? I think there's a fair bit of top down influence too. Europe wasn't that big an issue until it was decided there would be a referendum and the campaigns kicked in then suddenly the public felt it was.