Well Tony Blair did feel the need to do a Charles II and pretend to be Anglican while in office.
And that's just thinking about England. A lot of MP's in Scotland are religious, and it crosses over the parties. The Catholic Church pushes its agendas through the Labour Party, the Tories have ties with Unionism and the Orange Order, one caused controversy in refusing a gay couples access to his B&B, and the SNP had one councillor who recently called all gays sad people and said atheists were all going to burn in hell.
And that's without going into Northern Ireland, where they have a lot of very hardline Ian Paisley-esque Presbyterians, and some guys that have pretty quirky ideas (that they are descended from the 10 lost tribes of Israel etc).
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