The current (20060116) government wants to reform the way the top end of the British judicial system works. This is all tied up with reform of the House of Lords too.
At present, the formal structure is that the highest court to which appeals can go is the House of Lords, with the Lord Chancellor, who is head of that house, as the chief judge. In practice, it doesn't actually work like this: the judicial work of the Lords is handled by a bunch of old boys called the Lords of Appeal in Ordinary (aka the Law Lords), twelve very senior judges who have been elevated to the Lords specifically to do this job, and who do not (i believe) vote in the Lords' legislative business (although they do speak in debates, when judicial input is appropriate). Individual cases are not handled by all the Law Lords at once, but by Appellate Committees, which consist of five of them (or three, if the job is to decide whether an appeal should be heard in the first place, or seven or more if a really important case is being tried). The chief is the Senior Law Lord, and his deputy is the Second Senior Law Lord.
The key point here is that although the highest court in the UK is formally the House of Lords, it is in fact a different entity, which doesn't really have a name, and which is composed of senior judges rather than legislators. In other words, it's much like the supreme court of more modern constitutions.
There are a few wrinkles. One is that in Scotland, the highest court for criminal cases is something called the High Court of Justiciary, from which there is no appeal to the Lords; civil cases don't go to this court, but to the Court of Session, from where they can be appealed to the Lords. Bloody Scots - they have a basically completely bizarre legal system (although they do have the excellent 'not proven' verdict). The other is that for cases arising from devolution law, the highest court is the Judicial Committee of the Privy Council - appeals can come here from lower-level courts, both of first instance and appeal, and from the Lords. The JCPC is also the highest court for weird stuff like cases in ecclesiastical courts, Admiralty courts, and other sources that aren't proper courts, disciplinary hearings in the Royal College of Veterinary Surgeons, courts in the Channel Islands, overseas territories and suchlike, and also from some Commonwealth countries. To make things more confusing, the JCPC consists of the Law Lords, plus some hangers-on (certain senior judges from outside the Lords), so it's basically the judicial arm of the House of Lords in disguise.
The Lord Chancellor is worth another mention. First and foremost, he's the head of the House of Lords - he's a chairman, but unlike the Speaker in the Commons, he's not neutral, and takes part in debates. However, he's not Leader of the House - there's one of those as well. Secondly, as head of the Lords, he's nominally Chief Judge of the land, and accordingly, Lord Chancellors are usually high-powered QCs before getting into politics (very rarely judges, since judges don't get into politics, and most Lord Chancellors, AFAICT, are politicians). However, there is a very strong tradition that Lord Chancellors do not involve themselves in the work of the Law Lords - the position is purely ceremonial. Thirdly, he's a cabinet minister, responsible for constitutional affairs, leading a department once called the Lord Chancellor's Department, and now called the Department for Consitutional Affairs.
So what does the government want to do, and why? Well, basically, they object to the fact that there's overlap between a court and a house of parliament, and that one person is head of that court, that house, and a department of the government. Accordingly, they want to transfer the Law Lords to a new court, the Supreme Court, entirely separate from the House of Lords, headed by a President (equivalent to the present Senior Law Lord) and his deputy. They then want to have the Department for Consitutional Affairs headed by a normal minister. They then want to abolish the Lord Chancellor, and presumably just have a Speaker in the Lords.
Mostly, reasonable things to want. However, also a bit flawed. I think they're being too radical with the names, and with the separation of the court and the house. Also, they're missing some loose ends.
So here it is, that manifesto in full: