I really hate to ask this at such an especially bad time, but could one of you Brits give this confused Yank a very brief thumbnail sketch of the structure of the British government, especially as it contrasts with the US version? Whenever I think I'm starting to understand it, I realize I don't.
I know the main difference is we have a presidential system in which a separately elected chief executive runs a separate executive branch of government while you have a Parliamentary system in which the executive is the leader of the majority party in the legislature. While our elections occur on fixed timetables and it is intentionally difficult but not impossible for our Congress to get rid of the US president before an election, you have something called a "vote of no confidence" and seem able to call elections and change prime ministers on short notice.
As with many parliamentary systems, monarchical and republican, executive is vested in a head of state who does not in practice wield it. Instead, a head of government is derived from the lower chamber of the parliament, the Commons in our case, appointed by the head of state to wield it in her name. It would be like the majority house leader becoming president.
The individual who is appointed is the person best placed to command a majority in the Commons, which usually means the leader of the largest party. If that party changes leader, the Prime Minister changes without need for a general election. Internal party politics is probably about as common a way for the Prime Minister to change as a general election where his party loses MP's to the point that he stops being able to command a majority. In Australia, it seems to be a weekly ritual.
Until recently, dissolving Parliament to call an election was part of the Royal Prerogative, so could be done anytime the Queen felt like it. In practice, this meant whenever the Prime Minister asked her to. 5 years ago, the Fixed Term Parliament act ended that. Now to dissolve Parliament requires a super-majority vote in the Commons. Instead Parliament will expire after 5 years.
Every year, there is a Queen's Speech in Parliament, delivered by Queen by written by the government and usually accompanied by mêmes in the press suggesting the Queen is thinking little of what she is having to say. A vote on the Queen's Speech is a vote of confidence in the government and so if it fails (highly rare) the government is sacked and a new one formed. If necessary a general election may need to be called to find a new one. However, I'm not sure how this works in the world of fixed term parliaments.
I know that although we both have two houses in the legislature, our "higher" house is elected and yours isn't. Our system seems structured to perpetuate two dominant political parties because of a "prisoner's dilemma" type situation discouraging votes for third parties; in your system, multiple parties and coalitions seem common.
The Lords were originally supposed to represent the aristocracy, hence the name. The positions were hereditary up until 20 years ago. Now there is the thing called a life peerage where an individual is enobled by the Queen on advice of someone governmental and serves for life, but the position is not hereditary.
This is a great cause of controversy and Lords reform is on the agenda still. The Lords is one of the few upper chambers in the world which is bigger than the lower chamber, which is taken as a sign it doesn't work properly. Basically, whenever a government changes, the old Lords stay in place while new Lords are appointed to "better reflect" the new mandate of the people. This means more party apparatchiks and worse party candidates defeated at the ballot box but favoured by the party leadership getting enobled.
There is a drive for changing to an elected chamber, a sort of Senate in form if not in name, but the Commons are sceptical because they don't want the Lords challenging their supremacy. Being a pig's ear of a house allows them to function in their role of reviewing and revising legislation while delegitimising them to the point that they know who the real legislators are. Elections are also not universally supported because it is considered there is an advantage to getting people who bring certain expertise who are not normally full time politicians. The Lords does have a high proportion of cross benchers who do not have a party loyalty.
Our political landscape has fractured a lot of recent decades. The Commons is elected by First Past the Post, which means there are 650 constituencies who elect a single MP on the basis that whoever gets the most votes wins. This helps to keep the two main parties dominant but allows for local variations, for example nationalists in Scotland and Wales, while Northern Ireland has a completely different set of parties to Great Britain. This is also controversial. We had a referendum on voting reform a few years ago, which was resoundingly rejected.
So, what important differences did I miss?
So in summary, key differences:
Parliamentary vs executive presidency.
Separation of role of head of state and head of government.
Unelected upper chamber, which hangs in limbo for reform.
Governments can be toppled by general elections but also failing to get a Queen's Speech through Parliament and through internal party politics.