Can you have a Roman Catholic Prime Minister of Great Britain?

Answer 1

There is no simple yes or no question to this answer. While there is no express legal bar the election of a non-Anglican British Prime Minister, such a situation would be constitutionally akward given the prime minister's role in appointing senior members of the Church of England. While theoretically, the soverieng has the ultimate power in making ecclesiastical appointments, he or she acts on the advice of the prime minister.

Under the Roman Catholic Relief Act of 1829, sect. 17, and the Jews' Relief Act of 1858, sec 4, no Roman Catholic or Jew may advise the sovereign on ecclesiastical matters. Were the prime minister to be a Roman Catholic or a Jew and alternate system of ecclesiastical appointment would have to be devised.

To date, all British Prime Ministers to date, at least while in office, have professed Anglican faith. Disraeli, while born into a Jewish family, was babtised into the church of England at age 12 and Tony Blair waited till after he stood down from the post of Prime Minister to officially convert to Catholicism.
Gordon Brown does not 'profess the Anglican faith'. His father was a Church of Scotland minister. It is unlikely that any other non-English Prime Minister would be an Anglican (e.g. Alec Douglas-Hume, Ramsey Macdonald).