Sir Keir Starmer says Labour would aim to abolish the "indefensible" House of Lords - ideally within his first term as prime minister.
It's part of proposals outlined in a report from Labour's commission on the UK's future, which is headed by former Prime Minister, Gordon Brown.
Leslie Lord Griffiths is a Labour peer and a Methodist minister. He's been speaking to Premier about the proposals:
"The fact is that the House of Lords desperately needs reform, nobody denies that. Certainly not those of us who sit in it, but whether abolishing it and then replacing it with an elected chamber is the best thing is entirely up for grabs, because it will take forever to achieve.
"It will set up a very expensive second chamber of people who are not, as we are prepared just to scrutinise legislation. If I'm voted in, I want power to change things. Whereas the House of Lords at the moment can only advise the elected chamber. So once you've got a dual sort of house arrangement, you've got the possibility as in America, as in France, of having what they call cohabitation. That is you have opposition between the two houses and it could be pretty grim. But for all that it needs reforming."
There are currently 786 sitting peers, including 26 Lords Spiritual. Lord Griffiths says that the Chamber needs to be reduced in size:
"The Prime Minister, who has the prerogative to appoint people to the laws, keeps on stuffing the Lord's with his own friends. Get rid of the titles, that wouldn't be a bad thing. So that I could be Lesley Griffiths again, instead of this wretched Lord stuff. Because as a Methodist minister, I know there's only one Lord and it isn't me. But for all of that, I think that we should retire. We shouldn't be necessarily there for life, we should be working peers.
"We should bring the numbers down, and abolish once and for all, the hereditary principle, those things would make it a much smaller, more compact, more rational place for us to be."
Lord Griffiths is cautiously in favour of another of Labour's proposals - to form a new democratic assembly of nations and regions to replace the House of Lords:
"We have devolved governments in Wales, Northern Ireland, Scotland, who feel pretty distant from power. So the House of Lords might become constitutionally a place where the devolved governments can meet each other and across their separate regional identities, forge policies and interchange with each other, interact with each other in a way that they could be more productive. I personally could see it being a Senate of all the regions, for example, but that's not abolishing it to replace it with an elected alternative."
Labour says it will consult on all the proposals before deciding whether to put them in its manifesto.
"The document that we're talking about, sets this out as a proposal, and it's now going to go out for consultation, which equals long grass. So we'll see what happens when it comes back again."