what made you think that the PM was chosen by the party rather than the people?

I'm not sure. I had a government class way back in middle school and I'm positive some subconscious memory of how things actually worked stayed with me. I guess I thought it was analogous to say the American Speaker of the House or the Senate Majority Leader. Both of those positions are elected by the parties in power. So, a person votes for their own Senator or Representative, and then the majority party in each body elects a leader.