Proportional representation means the number of seats is directly proportional to the number of votes for a given party - if the party gets, say, 45% of votes, it gets 45% of seats. The UK and US don't work like that; we use a form of plurality known as first-past-the-post.
For example, in the US, Obama received 52.9% of the popular vote and about 68% of the electoral vote as a result of their bizarre first-past-the-post system - it's entirely possible in the US for a presidential candidate to lose the popular vote and win the electoral vote, and thus become president with less support than their rival.
Ostensibly we have a multi-party system. Realistically, we have a two-party system. While we have a much bigger third party than, say, the US does, they still don't actually stand a chance of winning anything.
Gordon Brown is from the New Labour party. The opposition is the Conservative party, and the third wheel is the Liberal Democrat party. We also have a handful of minor parties, some of which are big enough to be worth considering, namely the Green party (pro-environment) and the UK Independence Party (ultra-nationalist racist loonies).
We don't get coalition governments, primarily because of the first-past-the-post system (which in turn suppresses the power of parties beyond the major two). There's always an outright winner.
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