I have for many years wondered where contributors to Thought for the Day came from. I hope that even those who are friends of mine will forgive me for saying that they were rarely well-known before they were given this prime slot, and that even within their fields there are others at least as distinguished. I expect the "faith leaders" to be invited to sit in a "reformed" Upper House to selected by much the same means, whatever it is.
So, from my own lot, do not expect Fr Aidan Nichols OP, Fr Ian Ker, Fr John Saward, Fr Tim Finigan, or anyone like that. In which case, who, exactly? Dispensations would be granted from the canonical ban on clerics sitting as civil legislators, if the clerics in question met Rome's rightly stringent criteria of orthodoxy. After all, that ban is nothing very ancient: Catholic priests originally predominated in the House of Lords.
But the dinner party circuit presumably employed by Radio Four would almost certainly produce no one whom Rome would countenance dispensing. Ringing up, say, the Editor of The Tablet is a surefire way of producing a list of frankly unacceptable candidates.