The Crown Soundtrack

I would like to ask the same question as above. What is that piece, it is Beethoven, I have heard it numerous times, I just cant' remember the name. and it's definitely not the Moonlight.

Beethoven’s Moonlight Sonata

What does the young primeminister play on the piano in the first scene at 7:37?

I can’t seem to directly reply to the question above, but I can like this :) the piano song played by the young prime minister in Imbroglio (the Crown season 3 episode 9) at 7:37 is called Prelude no 15 ‘Raindrop’ op. 28 by Chopin. Depending on the recording, you’ll start to recognize what you heard on the episode from about 2 minutes in. Cheers!