THE House of Lords, Ed Miliband declared earlier this month, is "one of the biggest pieces of unfinished business in our constitution".

The most cursory glance at the inner workings of the second house of the UK Parliament shows why.

There are getting on for 800 members of the Lords. Most are appointed, in recognition of years of public service (or support for a party) by the Prime Minister or House of Lords Appointments Commission. But there remain 92 hereditary peers, including two performing the royal offices of Earl Marshal and Lord Great Chamberlain, who are elected by other members of the Lords.

There are also 26 Lords Spiritual whose seats come courtesy of the Church of England. If the UK had a written constitution, the chapter entitled "House of Lords" could have been penned by Barquentine, the Master of Ritual in Mervyn Peake's gothic fantasy Gormenghast.

Mr Miliband has promised to sweep away such anachronisms, which date through the mists of time all the way to ... well, to 1999 actually, when Tony Blair's Government removed most of the hereditary peers but kept the role and essential character of the Upper Chamber.

Ed Miliband's vision is for a American-style Senate, based on representation from the UK's nations and regions. The idea, a form of which was floated by Gordon Brown in his recent book My Scotland, Our Britain, is part of a wider devolution agenda, which also includes handing powers and funding to city regions and strengthening the devolved governments in Scotland, Wales and Northern Ireland. Replacing the historic House of Lords with a Senate sounds a radical step, but there is a lot we still do not know about the proposals.

The present House of Lords spends its time scrutinising legislation, holding inquiries into public policy and questioning Government ministers. These tasks would need to continue, even if they were pared back. But what of the Senate's possible function - outlined by Mr Brown - championing national and regional interests on the UK stage? That is all up for negotiation.

Under Mr Miliband's plans, the role of the new-look second chamber would be discussed at meetings in Edinburgh, Cardiff, Belfast and the English regions in advance of a UK-wide Constitutional Convention to be launched in the early phase of a new Labour government. The same goes for the number of senators and how they would be elected. These are both interesting questions in their own right.

In their failed bid to reform the Lords a couple of years ago, the LibDems called for the number to be cut to 450. Is that the right number? As for filling Senate seats, Labour favour direct elections, though, again, they will consult on different systems. There are also question marks over who would be eligible to stand (residence criteria have been suggested) and even where the new body would be based (the Palace of Westminster has not been ruled in for certain).

Mr Miliband's Senate is an intriguing piece in a constitutional jigsaw puzzle. But with only the sketchiest details of how might work, we are not yet seeing the whole picture.