The issue, obviously, is that no party that wins a majority with First Past The Post is going to change it. See Labour in 1997¹, who relegated it from a manifesto pledge to commissioning a report on it, which they largely ignored. Personally my preference would be for a system like the Scottish Parliament uses, and then have the House of Lords replaced with a (mostly²) elected chamber based on regional open lists.
I could talk about politics all day, and frequently do on other forums!
¹Ironically, given the above conversation about Jack's "I was only 9" business. I was 11 and paid some amount of attention to Blair, even at the time, but then I've been a politics geek for a long time...
²I'd include say 20 seats for appointed experts for each government department, plus - although I disagree with an established Church - you probably have to leave the two Archbishops there until you can remedy that, which is easier said than done.