This is nothing new. There's been enormous parallels between the two countries for decades now, even if the timing of that link has gotten a bit skewed of late.
Trading back and forth between two centrist parties in the first post-war decades, in both countries the center-left party, exhausted in spirit if not ideas, had its head handed to it at the end of the 1970s by the center-right party. Only now that starboard party was under the leadership of the radical right in Britain Margaret Thatcher, and in the US her ideological soul-mate, Ronald Reagan. They governed for a decade and bloody well wore out their welcome (notwithstanding the regressive hagiography of Reagan since he left office, their attempt to turn him into latter day deity).
Then, in the election which followed (1988 in the US and 1992 in the UK), the watered-down version of the far-right candidate (John Major and Bush the Elder) somehow, surprisingly, managed to thrash out the weakest imaginable endorsement and hold the keys to government for another term. After that came the other party with an even weaker version of the same politics. Just as Thatcher and Reagan were like peas in a pod, and just as Major and HW were nothingburger clones, so too the backward and oleaginous Tony Blair and Bill Clinton were twin sons of different mothers. Now it looks like Britain may be getting its barely-endorsed "compassionate conservative' to match our George W. Bush, in the form of the polished-up-to-seem-less-abrasive Tory David Cameron.
First, in these confused political times, people don't really know what they want.
Second, except that they definitely want everything.
Oh, and one other thing: there's that small matter of gross incompetence at voting stations (taking the most benign interpretation).
Nor are these tendencies, in their broadest sense, hugely different from other Western democracies. It's the Age of Ennui, really. Nothing seems to be working, and no solutions seem to be on the horizon. To be honest, the moment feels considerably volatile well beyond the scale of the hardly insubstantial problems facing these societies and the planet as a whole.
People are simultaneously looking for societal change, and yet desperately holding on to the status quo. People are simultaneously hungry for different party choices, and yet continuing to vote for the existing bums in office. People are simultaneously hungry for something very different in politics, and yet clinging on to the same old same-old.
In the UK, it looked for a while like they just might get a bit of some real shake-up, both small and large. The biggest development of this election cycle was the introduction of US-style televised debates, and the biggest product of that, at least initially, was that the leader of the half-party Liberal Democrats, who was allowed to share the stage with the Big Two, knocked them both sideways with his "they're-endlessly-petty-and-to-blame-for-everything-but-I'm-above-all-that" act. It worked for a while, though it had already lost its punch by the third debate.
Were the Liberal Democrats to come to power as junior partners in a coalition government, owing to the failure of either Labour or the Tories to win an outright majority of seats in Parliament, that alone would only represent minor change. Politically, there is little about the party that is remarkably different from the two majors. And that's before they get into government, when the drill is to promise the world. Imagine what it would be like afterwards, when instead it's all about figuring out ways to not deliver on your promises.
The big change in the UK could entail the use of a proportional representation system to replace or partially replace using a hybrid system the district model. That could have very significant longer term repercussions with respect to the distribution of parties in the British Parliament, and the possibility for smaller ones to not only flourish, but perhaps even govern at some point.
None of that will happen in the US, however. First, because there is no significant third party to hold some other major party hostage in exchange for a restructuring of the national electoral system. But more importantly, because it would be far less relevant even if there were, since the executive branch of American government does not require any form of legislative majority to be elected. Such a system might work in determining the leadership of one or both houses of Congress, but the president unlike the British prime minister is elected entirely separately. If the US kept its Electoral College system, the only way third parties would matter is if no candidate hit the magic number and the parties then got into some serious horse-trading for electoral votes. And if we moved to a system of electing presidents directly, on the basis of winning a plurality of the popular vote, or even a majority run-off system, third parties would have little or no effect.