An actor as British PM?

Is there any plausible cases where a British actor or actress - either famous or minor - could become PM of the UK?

Easy!

1. Alec Guinness decides he wants to be PM of the UK. (Why? Who knows...)
2. He makes a quick stop by the makeup and wardrobe departments. In addition to other necessities, he acquires a large blunt instrument.
3. He sneaks up behind the current PM in a dark alley and bashes his skull in. He hides the body, and assumes the role of "The PM of the UK".
4. Alec Guinness vanishes, much to the dismay of the movie-going world. The PM of the UK is noted to have grown/shrunk by several inches according to a story in the Mirror, but few pay it much attention.

Hey, nothing said the actor had to become PM by legal means!
 
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