This is a textbook example of a "False Dilemma"-type fallacy. Either don't vote for the PM or vote for "more than a hundred" ministers. Those aren't the only two options and you know that.
A vote for a PM could, implicitly, be a vote for the ministers that the PM would select. You select the PM, the PM selects their ministers and cabinet, that gives the public more Democratic power.
> I think in UK politics talking about apathy and ignorance is often a nice way to talk about other people's ignorance of your better opinions, and their apathy for your better ideas.
Three quarters of people 'cannot name their local MP'[0].