It could have been much worse. Most Europeans, even conservatives, were dreading the prospect of President Mitt Romney, an obvious fraud whose voters are angry ageing white men and whose sponsors are half nasty and half crazy. And there was an almost worse prospect, of a rerun of 2000 and the grotesque farce in Florida – or alternatively of Barack Obama winning a majority in the preposterous electoral college but not a majority of the popular vote, and having his legitimacy challenged by the Republican for the next four years.

Even as it is, the situation in Washington is bad enough, as the re-elected Obama faces a bitterly hostile House of Representatives, yet again a dismal reflection of the American political system. No doubt anti-Americanism can take odious forms, but pro-Americanism is almost more curious. Not only the Anglo-neocons infesting the Tory party but some Labour politicians – Gordon Brown as well as Tony Blair – and liberal pundits are infatuated by all things American, including their written constitution, and a political culture which we are told we should emulate. To the contrary, without being complacent or excessively patriotic, I suggest we have nothing at all to learn about politics from across the Atlantic.

In their way, the founding documents of the American republic are very remarkable. The Declaration of Independence, the constitution and the Bill of Rights are written in limpid Augustan prose which can be read for literary pleasure, a contrast indeed to the equivalent documents of the European Union, from the Treaty of Rome to the abortive constitution, with their rebarbative bureaucratese. And never mind the fact that the declaration demands a free hand to deal with "merciless Indian savages" or that the constitution implicitly recognises the institution of slavery.

The trouble was that the constitution was set in stone, or at least on parchment. A political system designed by a group of 18th-century country gentlemen and radical artisans, with its various expedients and compromises, including the fiction of the electoral college, is supposed to work for all time. Meanwhile, what the Victorian writer Walter Bagehot called "the English Constitution" had evolved out of all recognition, and rather brilliantly. A country ruled in 1830 by a narrow oligarchy supported by a corrupt House of Commons, for which only about one in 20 male citizens could vote, became, within 100 years, a full democracy with every man and woman over 21 enfranchised.

By the late 19th century, our unwritten constitution was distinguished by two excellent features that America does not possess: constitutional monarchy and parliamentary government – the monarch reigned but did not rule, and the prime minister was whoever at that moment commanded a majority in the lower or representative house, which we call the House of Commons. That was true of the age of Gladstone but not 100 years before, when George III was his own chief executive, and could appoint Pitt at his pleasure without concern for any parliamentary majority.

And that explains an unremarked but curious fact. While the American founding fathers were in conscious reaction against England, they unconsciously echoed its political culture. With the constitution cementing that in place, it means that American politics today is closer to British politics at the time the Americans rebelled than British politics today, and Obama resembles George III more than David Cameron (politically rather than personally, that is). He is both head of state and chief executive, and does not need, or indeed now have, a congressional majority. Like the king, he has to barter with the legislature, using cajolery, bribery or appeals to loyalty (the last not much use with the present house).

The resemblance goes even further. Congress is more like parliament under George III than under George VI. The House of Lords may be absurd, but it is not more absurd than the Senate. Wyoming, with its 570,000 inhabitants, sends two senators to this bizarre body, and so does California, with 40 million. Even worse, since the 17th amendment of 1913, senators have been elected by popular vote. Until then, they had been chosen by state legislatures, as is still true elsewhere.

During arguments over our own House of Lords it was said we were the only country without an elected upper house, which is quite untrue. In federal countries the upper houses represent not the people but constituent states: the Bundesrat in Germany consists of people not elected by voters but chosen by the governments of the Länder. Direct election of the Senate conferred a wholly unjustified appearance of democratic legitimacy on a wildly unrepresentative body.

As for the House of Representatives, it's an American version of the corrupt, unreformed Commons so memorably dissected by Sir Lewis Namier. Although the house is elected every two years, a high proportion of individual districts are effectively uncontested, with only a minority of citizens voting. This month's turnout in the presidential election was actually over 60%, which is high by American standards; in the midterm elections two years ago it was 41%.

And anyone who thinks that the recent wrangles here over our constituency boundaries were unseemly and driven by party interest should gaze across the Atlantic, and look at maps of the weirdly shaped congressional districts, carved out for naked partisan purposes. The third district of Maryland has been called the most gerrymandered in the nation, a "crazy quilt", as the Washington Post calls it, or as a federal judge put it, a "broken-winged pterodactyl, lying prostrate across the centre of the state".

If the American system is antiquated and dysfunctional, that dysfunction is preordained. Institutions designed 230 years ago for a handful of almost entirely agrarian colonies on the Atlantic coast with a population of fewer than four million (including slaves) are supposed to operate in a vast, advanced industrial nation of 314 million. Is it any wonder they don't work? And mightn't the Americans have something to learn from us, rather than we from them?