Nebula

The Lords cannot ultimately block legislation

But that's just the thing: its defenders have good points about its purpose. But being unable to block legislation undermines their case. To the extent that their arguments are correct (that the Lords really do spend more effort thinking deeply about issues and using expertise to decide what's best to do, regardless of political popularity), being unable to block legislation undermines that.

First Past the Post is a much bigger problem

Absolutely. I actually think Lords reform could be a backdoor way to improve the electoral system. If Lords was replaced with a House of Nations and Regions (which...seriously? Just call it a Senate. That's literally the one thing in common between the Senate in Australia, America, and Canada...), having it be elected proportionally would be a much easier sell than changing how the House of Commons is elected, considering the fearmongering and failed past attempts to overhaul the FPTP system.

And then, maybe, once they've seen the HoNaR's (ok, I do kinda like that acronym...) proportional system work well, maybe it'll be harder to oppose reform to the Commons as well. But even failing that, a proportionally-elected upper house with real power would offset a lot of the harm of an FPTP Commons, in the same way that Australia's proportional Senate offsets the problems with single-winner IRV in the House of Representatives.