As the litter is swept up at the Olympic stadium, as the members of Her Majesty's armed forces are returned to their barracks and Lord Coe departs for a well-earned holiday in Frinton, the last rite of the 2012 Olympic Games will begin to be performed. This is the long awaited groundswell of liberal unease over what might be called the paraphernalia of contemporary patriotism.

The Union Jack, a collection of somewhat anguished voices agrees, has been "redeemed" – that is, snatched out of the undesirable grasp of the xenophobic and/or militaristic right and turned into a multicultural symbol. But what of the National Anthem (a "dirge" according to The Independent's Dominic Lawson), which continues to be criticised for its belligerence, religious overtones, neo-imperialism and so on? Should we, as one or two opinion-formers have suggested, commission a new one more sensitive to the realities of life in 21st-century Britain?

Fresh from a sporting event in which we have had a chance to hear some of the other national anthems doing the rounds, I can't help feeling that this is a very bad idea, the worst idea, as a character in a Martin Amis novel might say.

The National Anthem may very well peddle the antediluvian notion that God is essentially an Englishman, but it takes only a bar or two of one of the newer effusions from the Commonwealth to hint at how anodyne a modern, secular anthem would sound, particularly if its overriding aim was less to exalt the country it described than merely to avoid giving offence.

Much the same principle applies to The English Hymnal. All Things Bright and Beautiful is as out-of-date as a cloche hat, but I never met a churchgoer who preferred to sing one of those "contemporary" hymns which have "Copyright Kingsway's Thankyou Music" at the end and are full of arresting couplets of the "Jesus you are very nice/Of course you had to pay the price" variety.

A realist might even wonder why the long-censored verse about frustrating the knavish tricks of our enemies and confounding their politics couldn't be reinstated. As patriotic Britons, surely we want our enemies' politics confounded, and it is hypocritical of us to pretend otherwise.

Along with the stirrings of liberal disquiet over these signs of patriotic fervour, there has also been a great deal in the press about the "unifying" effects of the Games and their secondary function as a kind of societal glue, able to knit together what is not so much a fractured nation as a defiantly heterogeneous one. Much, therefore, was made of the BBC's announcement that well over 20 million people had tuned in to the spectacle of Usain Bolt cruising to victory in the men's 100 metres.

Although not quite as eye-catching as the 28 million viewers thought to have watched England beat West Germany in the 1966 World Cup Final, or the near-identical figures racked up by the Morecambe & Wise Christmas Show in the 1970s, this is an impressive statistic from a world of ever-proliferating TV channels and consumer choice. All the same, it makes you wonder what the other two-thirds of the UK population were doing at the time? Watering their bedding plants? Walking the dog? The myth of a collective consciousness, or even the idea that everyone on a specimen high street has approximately the same kind of internal data available to them, is horribly seductive. In reality, you suspect that significant numbers of people get by in the absence of facts that most of us regard as vital to our existence.

Back in the 1980s, for example, at the height of the Thatcherite project, newspaper surveys regularly threw up the information that several per cent of those questioned could not identify a photograph of Mrs Thatcher. Intensely disapproving of this at the time, I now think there something rather heroic about it, a refusal to be dragooned into the routines of mainstream life, a kind of quietism by default, whose underlying attitude – that what is important to you may not necessarily be important to me – is always bracing. As Douglas Dunn put it, in one of his "Terry Street" poems from back-street 1960s Hull, "There are many worlds, there are many laws."

Local newspapers sometimes have a curious notion of patriotism. As George Orwell notes in Keep the Aspidistra Flying, they are generally "so avid" for a local angle that "such items of news as 'Hampstead Man on Murder Charge' or 'Dismembered Baby in Cellar in Camberwell' are displayed with positive pride".

Here in Norfolk, the Eastern Daily Press has been making a commendable effort to give its readers a whiff of the Olympian spirit. On Monday, it managed to turn up the parents of the sprinter James Dasaolu, who run a newsagent's shop in Witard Road, Norwich. By Tuesday, the news that the horse Big Star, ridden to triumph by Nick Skelton, was actually owned by a couple in north Norfolk covered the front page.

All this was par for the course. On the other hand, true East Anglians will have been a little bemused by BBC Look East's lavish account of the jamboree that took place in Milton Keynes to welcome home local boy Greg Rutherford, winner of the men's Long Jump gold, on the excellent grounds that Milton Keynes is in Buckinghamshire.