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Not a bad question - do you wear different clothes for different purposes, and what is the significance ?
Buenochico as usual is firing on all guns (he in Teneriffe or somewhere)
The bishops are there as a result of their office - ex officio and not because of their name (Freddie Bloggs) which I think is in personam
I think some of the 26 rotate - Archbish of Canterbury - or +Cantuar as he calles himself - doesnt but I think Bath and Wells does for example
The Irish Peers that were, did used to elect themselves - the last one was 1922 because the Lord Chancellor of Ireland had to preside over the election and his office was abolished.
You cant be ordained and sit in the House of Commons - as that would imply two votes in an election - one for the MP and one thro the now separate org of Bishops called congregation.
I googled Eccl Commissioners of England and instead of getting a freehold covenants case, instead got the High Court agonising over this very point.
and it was the ordination bit that did it - Roman Catholics were included in the ban but Quakers (no clerical orders) werent
It dates from the time when Religion was thought to be an acceptable subject to legislate about. Act of Uniformity and so on
Church and State are not separate in this magnificent democracy, whereas they are in other countries - Republic of Ireland for example
and if your French is O level google 'laicite' in French WIki