The big problem with an elected Upper House is that sooner or later - and likely sooner - an elected member is going to say, "I have a mandate from my electors to do X; I was elected on this platform." Cue crisis.
Let me put forward the start of an idea:
1. The Upper House is now called the Senate, members are Senators. Senators are wholly appointed.
2. There are Senators Spiritual (widened to more than the CoE), Legal, and Military, just as now, perhaps more formalised.
3. MPs who have been members of the Privy Council, Speaker, or have served for 20+ years and have chaired a Select Committee may become members upon retirement or losing their seat in the Commons.
4. MPs and recently ex-MPs may become Senators by appointment by the Prime Minister (as at present). Note that the PM may not appoint people who are not MPs or recently ex-MPs. That should cut down on the selling of honours.
5. There should be an independent commission to appoint Senators from outside the political arena who should be leaders of their fields and are prepared to contribute. There should be a limited number of such Senators and those who make up the recommending body should be forbidden from political appointments and positions for 20 years.
6. Just as in the Roman Senate, Senators should be subject to review, and those who do not ahem Ashcroft or cannot participate should lose their positions.
7. Public disgrace ahem Archer should also result in losing one's seat.
8. ...
It's not much, but it's better than what's been presented.