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I'm guessing he prefers an elected upper chamber.

I'd continue with hereditary peerages but I'd just make them titles only, not an entitlement to sit in the House of Lords. Who cares if Baron Cuntface passes down their title to their eldest spawn if they die.

Pick a cut-off date in the next few years, any hereditary peers that die after that date only pass down the title and not the entitlement to sit in the house of Lords and, once numbers come down to a more sensible figure we start having elections to replace the ones that pop their clogs (or the ones that resign or time out if we have them elected for a finite term).

Heriditary Peers lost the right to sit in the House of Lords 25 years ago.
They still vote amongst themselves for 92 seats