In Burke's 1787 coining he would have been making reference to the traditional three estates of Parliament: The Lords Spiritual, the Lords Temporal and the Commons.
In 1688, the issue arose during the trial of the Seven Bishops—William Sancroft, Archbishop of Canterbury; Sir Jonathan Trelawny, 3rd Baronet, Bishop of Winchester; Thomas Ken, Bishop of Bath and Wells; John Lake, Bishop of Chester; William Lloyd, Bishop of Worcester; Francis Turner, Bishop of Ely and Thomas White, Bishop of Peterborough—by a common jury.
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Since the House of Commons (Removal of Clergy Disqualification) Act 2001, no clergy except for Church of England bishops (see Lords Spiritual) are now prohibited from serving.