It might have been Viscount Castlereagh, in 1822, but I don't think he was ever PM, only Foreign Secretary. This is one of the bits of useless information I remember from school history lessons in the 1950s!
Lord Castlereagh committed suicide in 1822 - believing himself being blackmailed for his homosexuality. His friends and family knew he was likely to do this and had removed all razors etc but had overlooked his penknife. But as Iolanthe says, he was never Prime Minister.
Thanks for all your help! The question was on our staff xmas quiz, its baffled everyone ... think ill just put down the penknife chap, see if i get that bottle of wine! =)