Americans may not fully appreciate the differences between the US and the UK systems. The most important is that the US system was deliberately set up to have lots of checks and balances. If you like, think of them as safety catches and damping mechanisms. The UK system has just about none of these.
If you look at a UK election, you see that one of three things has occurred to bring it about. One, the government of the day decides to call one. It can do that any time, and this is a very powerful weapon, as it can time elections to coincide with upsurges in the polls, caused by, among other things, short term financial booms. Two, it loses a vote in the legislature on some important issue. Three, it comes to the end of its term, which is a maximum set in statute. There is no minimum term. The UK does not have fixed length terms.
Once elected with a majority of seats in the legislature, the party winning now owns both the legislature and the executive. The leader of the party becomes Prime Minister, with something like presidential powers. There is no doubt of his/her ability to get legislation through - he has a majority in the legislature, and it was that which got him to be Prime Minister.
There is no written constitution. Parliament, by a majority vote and consent of the monarch, can pass any legislation at all. If it wanted to (for example) repeal Habeas Corpus, it could. If it wanted to implement rule by decree, it could. If it wanted to leave the EU, it could. There is no safeguard of any sort of civil liberties or human rights from an Act of Parliament. It could, to take a ridiculous and extreme example, legalize slavery. There is no constitution to be modified by a complex process of two thirds majority voting, it just needs a majority vote in the legislature, and its done.
The US of course is completely different. Various bits of the governmental apparatus are elected from time to time - there is no equivalent of a general election of the kind the UK has just had. Only part of Congress or the Senate is elected in any given year. And when the legislature is elected, it does not get to specify who is the President, that is a completely separate election process. The legislature and the executive were deliberately separated by the Founding Fathers. The result is that the process of getting legislation through the legislature is quite complex and difficult, and subject to delay and prevention. In effect, the US is most of the time in a sort of coalition government, in UK terms - one in which negotiation with other parties is necessary, for the party in charge to get legislation through. This situation is one that happens very rarely in the UK, the party in power can almost always get its legislation through at once.
So, in this system, the debate about proportional representation has a very different force from what it would have in the US. Winning an outright majority in the UK gives a party a degree of power in both executive and legislature that can only be dreamed of by a US President. This is what neither Labor nor the Conservatives are prepared to relinquish, and why only desperation to get into or stay in power would lead them to make the necessary concession on PR to get into bed with the Liberal Democrats.
Right now the Liberals have some 23% of the vote and 57 seats in the legislature. If the UK system were truly proportional, and seats were in proportion to share of the vote, the Liberals would have around 150 seats and the other parties less. Conservatives now have 206, they would have under 200. Labour would be, on their current share of the vote, in the low 200s.
The end result would be, as in Holland, that the Liberals would be in every government, with one of the other two parties as partners. In Holland, this role is played by the CDA. The effect of this is that by very different means you have a sort of check and balance which is similar to that which the US system imposes. It becomes very hard to loot the country and divert the proceeds to your special interests, whether they be the bankers and landowners, or the trade unions. As soon as you go too far, you lose the centre, the government falls, and the centre party goes into government with the other guys.
As I write, the Conservative Party has offered the Liberals a referendum on one particular form of PR - something that always was anathema to them in the past, which is a measure of their desperation to get into power. The Labour Party has offered in reply a form of PR by means of primary legislation, no referendum. Which is also a measure of their equal or maybe even greater desperation.
In effect, what we have is both of the two large parties pawning their future to get power now. If they really were to enact PR, their future would not be, as they are now dreaming, absolute power by a total majority. It would be at best being the senior partners in coalition governments for the indefinite future. However, politicians rarely think beyond getting office, and these guys are no exception. They are probably thinking, we'll deal with that when we get to it, we'll wriggle out of it somehow.
Its going to be an interesting couple of days going forwards.