Re: Pleadings of TM
It used to be the case that a Catholic could not hold any public office including Prime Minister, but this was changed by the Catholic Emancipation Act of 1829. There are still a few offices that a Catholic cannot hold (chiefly the Monarch and the Lord Chancellor), but a Catholic can hold most civil offices, including Prime Minister.
We have never had a Catholic Prime Minister (Blair did not convert until he left office). To have one would present some difficulties. For example a Catholic Prime Minister would not be able to advise the Queen on non-secular matters.
This could be circumvented by having the Lord Chancellor (who cannot be a Catholic) taking on the role of the Monarch's adviser. But this also presents difficulties. The Lord Chancellor is a member of the Cabinet, and could be deemed as being influenced by the Catholic Prime Minister.
Simplest way is not to have a Catholic Prime Minister in the first place.