That is only half the story, presented in such a way that it is - IMHO - closer to false.

I really balk at these fatalistic one-liners. Voters vote for packages of politicians and views. Particularly in the UK with its silly voting system there are very few options for voters to tell the politicians what they feel with any acceptable degree of nuance.

Politicians do stuff the majority disagree with all the time. That alone shows your statement to be false.

A common issue is, of course, that the solutions politicians come up with for problems we want solved, doesn't always agree with us.

E.g. the fact that we do not want paedophiles in our lives doesn't mean that we want the politicians to cover up scandals like Jimmy Savile. It is a perversion of intent. Or would you claim that that is what the voters demand?