The Catholic Prime-Minister bit got me googling, and it isn't quite right…
"Incidentally, the 1701 Act of Settlement still prohibits British monarchs from being, or marrying, a Catholic. While there is, theoretically, no bar on the Prime Minister being a Catholic, a Catholic Prime Minister is considered to be 'constitutionally awkward' since that office is involved in appointing senior members of the Church of England."
Still, I didn't even know it was 'constitutionally awkward', so you live and learn.