The 1829 Catholic Emancipation Act allowed catholics to be appointed to most crown offices, except Lord Chancellor, Keeper of the Great Seal, Lord Lieutenant of Ireland and High Commissioner of the Church of Scotland.
Since the Prime Minister is still involved in appointing senior members of the Church of England, it is considered by some that a catholic Prime Minister would be 'constitutionally awkward.'
http://www.dukesofbuckingham.org/topics/politi cs/catholic_question.htm