Draped around gold medallists' shoulders or waved by ecstatic Olympic and Paralympic crowds, the Union Flag has enjoyed a high-flying year. In a tweaked version like a boy racer's go-faster stripes, it has offered a backdrop to speakers at the Labour conference. Next week, when the Conservatives meet, it will flutter again. Now imagine a country that lacked this bedrock insignia. Would it even feel the same?
One chapter in Neil MacGregor's new book, inspired by a section in the British Museum's current exhibition, goes back to 1604 and the heraldic designers' nightmare. They had to devise a flag for the two conjoined kingdoms after James VI of Scotland had become James I of England. "How difficult it is for us now to imagine the foreignness of the two countries, and the conceptual difficulty of putting them together," the director of the BM says. "If you've never seen a Union Flag, it's extraordinarily difficult to see how you get these two countries as one."
The book, Shakespeare's Restless World, illustrates the botched attempts to overlay or juxtapose the crosses of St Andrew and St George. As MacGregor writes, "you can see the intractable politics of union being played out in graphic form". The "one nation" beloved of so many politicians has always been easier to invoke than to achieve, or even to depict.
We talk in his calm and spacious office, at one side of the institution he has steered for a decade. The North American flora of the latest pop-up garden in the museum's courtyard are just the most recent signs of the global perspective he has imported into its work. However, his book, the Radio 4 series it expands and the exhibition (Shakespeare: Staging the World) manage to make our own cultural backyard look quite weird.
About that flag: MacGregor – the son of two doctors, schooled at Glasgow Academy and originally an advocate at the Scottish bar – reflects that its bungled prototypes embody all the pitfalls and flashpoints of the attempted federation of England and Scotland. "This really is trying to put two alien elements together, and nobody knows how to do it." In many ways, we never did crack that one. The church, the law, education: all proved incompatible. As for the ever-disputed union of parliaments in 1707 - come 2014, with the proposed referendum on Scottish independence, and the tricky banner may begin to tear apart again.
Shakespeare's Restless World shows time and again how the epoch-making changes that the Stratford playwright both lived through and expressed still echo through our arguments and anxieties over community and identity. And, as the Olympics proved, great events have a habit of putting all that unfinished business on the table again. MacGregor wants us to see both how the past shapes and shades our present but – equally – how strange and alien it should feel. "It is about the otherness of elsewhere, isn't it? What is the same and what is different."
For him, this twin perception of kinship and estrangement comes close to the core of his job as curator and impresario of other worlds. "The trick of the museum is, and from the beginning has been, to show the ways in which different people are like us. That's what that 18th-century idea of getting things together is."
As for the citizens, nobles, priests, plotters and merchants we meet via Shakespeare's words, and in iconic objects from his age, "In key respects, these people are probably very like us. But in others they can think the world in a quite different way."
Faith, and its fierce demands, can mark out those dividing-lines with unrivalled clarity. Among the exhibits the book discusses are relics that testify to the secret practice of Catholicism in Elizabethan England, as the queen's network of spies, torturers and executioners sought to suppress the old religion. From the grisly talisman of "Oldcorne's Eye" – the "oculus dexter" of a martyred Jesuit – to the pedlar's trunk that hides a priest's vestments and materials for Mass, we return to a time when dying for a faith remained a local custom.
The quest for martyrdom, MacGregor stresses, was an entirely "indigenous" pursuit for English Catholics. "To be brought back closely to people who are now part of the fabric of our society but who at that stage thought of this as a proper way to behave is, I think, a very powerful way of understanding better what is going on in many parts of the world today – not just on the Islamic side of this parallel, but everywhere people believe so strongly that to meet death for faith is a desirable outcome." On this soil the pious fought, and died, for their God. "This is a totally British way of behaving, only 400 years ago."
Yet Shakespeare, MacGregor argues, was born into a country changing faster than ever before – or perhaps since. "The gulf between the experience of children and of parents and grandparents in England, if you're born in the 1560s, is probably wider than at any other point until well into the 20th century." He asks: "Is that why we get this extraordinary drama in England - because England is so dislocated between the generations?"
With its keen scrutiny of globes, charts and maps in the first age of oceanic adventure, the book brings home the shock of realising that other cultures, of great sophistication, lay just beyond your ken. "We can manage the religious upsets, the religious violence, the disjunction of parents from children," says MacGregor. "I think what we probably can't recover is the fact that, suddenly, most of the world is unknown. We don't even get it with space." MacGregor, now arguably the most influential public intellectual in the land, came to the BM after 15 years at the National Gallery. Since the move, his own globe-spanning vision has challenged insularity of every kind. Not only has the Prospero of Bloomsbury staged a spellbinding parade of shows that open up other epochs and cultures - China to Mexico to Rome. He has repositioned the venerable old barn as a vanguard site of cosmopolitan thinking, at the heart of a globalised metropolis. So, in contrast to the mingled desire and dread with which Shakespeare's coevals greeted new worlds and new people, have we learned to live at ease with plurality?
On the one hand, he says, referring to the festive embrace of the Olympics, "Everybody in the UK now has experience of people living in different traditions – and broadly, the experience of living peaceably and even genially" with them. Yet some of those former rifts and fears persist. "You could argue that we no longer have a model of living genially with people who regard these issues of faith as so important that they're worth dying for. For most people in Britain, I think that is still a very hard position to understand."
Another chapter conjures up the pre-coronation spectacles of March 1604, during which James I rode in neo-classical triumph through London. In late 2012, one can't help but think of the Olympic ceremonies (not to mention the Diamond Jubilee). "That's what's interesting about these pageants," he says. "As a nation, we need them. We articulate who we are through these… artificial public shows. And the public need them, take part in them, enjoy them". Yet, within 40 years, the "unstable equilibrium" that James inherited had fallen into bloody pieces with the civil war. That pageant of national harmony, however brilliant, proved insubstantial. This restless past may present a dark glass through which we can view our own condition. But "I'm not sure we've got much further forward," says the BM's own master of ceremonies. He laughs. "The point of all these things is that we keep confronting the same problems – and we find differently inadequate solutions."
'Shakespeare's Restless World' is published by Allen Lane (£25); Shakespeare: Staging the World continues at the BM to 25 November