I am unsure about May. I was very much against her as Home Secretary (though I wouldn't claim she was incompetent) but I had a lot more time for her as PM.

I find it difficult to believe that no PM before the current administration* made the bottom five.
My first hand knowledge only goes back to Callaghan and I can only give guesses at other candidates. I would not be surprised if Callaghan had been suggested - I don't think he was bad, but I have heard it suggested by people who maybe should have some judgment. If there is anything positive to be said about Chamberlain, I have never heard it.

If the last five PMs are really the worst, does that say more about the period than about the five ? Should I mention the phrase "social media" ?

* polling is still open as I type this.