Well, as a thoroughly biased observer I would disagree with the idea that the Labour party is "socialist" - the
Political Compass site depicts Labour as being definitely on the right, which is certainly my perception.
The two main parties for the last few decades have been the Conservatives (Tories) and Labour. The Tories used to be fairly well-represented across the UK but since Thatcher (late 1970s) have adopted a more US-style brand of conservatism based on free market fundamentalism and "small state" rhetoric which seems to appeal mainly to (southern) English voters for some reason. The Tories are now probably similar to your more moderate Republicans but generally not so obsessed with religion/guns/sexual politics. The Labour party used to be a fairly left-of-centre party with close ties to the trade unions but after several defeats by the Tories in the 1980s/90s, they adopted the deliberately vague "New Labour" brand and have spent the last 20 years shifting to the right in order to try and attract conservative votes in England. These days Labour probably look like the leftward end of your Democratic party.
Since 2010, we have had a coalition government between the Tories and the minority Liberal Democrats, but this coalition has not been great for the Lib Dems, as many of their voters felt betrayed by Lib Dem support for Tory "austerity" policies, and their vote collapsed in this election.
The election is a big deal, partly because the opinion polls and chattering classes got it so wrong, and partly because it means we now have a rightwing Tory government with a clear majority in parliament (based on only 37% of the actual votes) to implement its policies without being constrained by the Lib Dems.
It is also significant because for the first time in a generation, the Scottish electorate has been able to vote for what they perceive as a genuine left-of-centre party - the SNP - instead of the Labour party, which many people view as "Tory Lite". Around 50% of the Scottish electorate did so, which means Labour, Conservative and Lib Dem parties now have only one seat each in Scotland while the other 56 Scottish seats belong to the SNP. The SNP does not stand outside Scotland, so this creates a strong gap between the Scottish political landscape and the rest of the UK. We now have a large Scottish bloc of SNP seats, but the UK government is controlled by the English-based Tories, which will definitely create some interesting tensions in the next few years and may well lead to demands for a fresh referendum on Scottish independence if Scottish voters see no way to influence the UK government. I suspect if there is such a referendum, then we will see the break-up of the UK this time.
Another reason why this is a big deal is because the Tory government is committed to an "in/out" referendum on membership of the European Union in the next couple of years. This is an issue which divides most political parties (except for UKIP which only has one policy: leave the EU), and is likely to dominate much of our political debate for the next couple of years.
[Edit:] If England votes to leave the EU, but Scotland/Wales/Northern Ireland vote to stay in (which is distinctly possible), then this could be another pressure leading to the break-up of the UK.
All in all, this election result feels pretty disastrous to a left-of-centre, UK federalist, pro-European like me. YMMV, I guess.
Incidentally, you can still fill in the questionnaire on
Position Dial to see where you might fit on the UK political spectrum. It reckoned I would be an SNP voter (probably correct), but unfortunately I don't live in Scotland!
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