At Elizabeth I's coronation, the crowd snipped pieces from the blue carpet she walked upon, even as she tripped over the raggedy holes they had created. They kissed her hem as she passed, frantic to thumb even the smallest thread of the accoutrements of power. These days, it's much easier. You can just bid for one of Margaret Thatcher's power suits, for example, at Christie's on Monday. And don't worry if blue isn't your colour: they come in yellow, pink and green as well.

Whatever you think of her politics, you can't dispute that Thatcher is an important part of 20th-century iconography. Even the greatest prima donna can become an icon – just look at Mariah Carey. Thatcher was one in the Churchill mode, never seen without her trademark sartorial armour and Scargill-proof pompadour. The undying influence of those who ascend to this level of visual familiarity was proved when, upon the release of the Meryl Streep vehicle The Iron Lady last year, I was bombarded with "Get the Look!" emails pushing pussy-bow blouses and box bags on unsuspecting – and more worryingly – politically unaware customers.

Who were they to know that buying into this was to assume the trappings of the North's oppression? That tying the silky knot around your neck was a very mockery of the noose that Thatcher set in the deregulated City of the Eighties and which is only now sliding into choking and eye-bulging grip as we come to understand its legacy? This was Iron-Lady dressing with all the Lady and none of the Irony.

Focusing on how someone is dressed – when fashion is not their primary purpose, of course – is a simple enough way of undermining their power. We do it constantly, from analysing exactly how high former President Sarkozy's Cuban heels were to laughing at Dave wearing his office shoes on the beach. When William Hague wore that baseball cap, it was a gift to his detractors because finally – finally! – he had managed to enunciate once and for all exactly how much of a loser he was. Without their having to say it.

But that's the way of it only because politicians are not icons any more; they're too exposed, too available to long lenses in their civvies. Like the great tragic heroes of classical antiquity, they've fallen off their perch and become just a bit anodyne and pedestrian like the rest of us. The only way to create an impression as enduring as the one that Thatcher made is to do a Lady Gaga and live in character all the time, which was Thatcher's precise tactic – although it didn't mean wearing fishnets.

What holy relics do we have from her successors? What would we bid for at auction? Not much: John Major's Y-fronts, perhaps, or Tony Blair's denim shirt. They were not resonant enough, and were not prominent enough, to create the sort of cult of personality that Thatcher achieved. As my father remarks, Major's superpower was to turn the whole TV screen grey. But even now, Thatcher's image endures – among a generation that never even suffered under her cosh. People will pay thousands for these suits, just like those villeins chopping up the ceremonial rug.

It might seem depressingly inevitable that the legacy of our most famous female politicians, our only female premier, should come down to a selection of skirt suits worn for television appearances, diplomatic events and baby-kissings. What else are the current crop judged on but their appearance? There's little likelihood of Theresa May's outré garb becoming collectors' items, nor Louise Mensch's smart but drab grey suits going under the hammer. It's incredible to think of a modern female politician wearing anything so expressive of their gender (The colours! The trim! The downright girlishness!) as these archive pieces. You get the impression none of them really could.

Just as Louis XIV made himself the Sun King, just as Elizabeth Tudor became the Virgin Queen, Thatcher created an image for herself, and that image has become eternal; it resonates powerfully, whether it makes you feel jingoistic or jangly.

But familiarity doesn't always breed contempt: there's something rather warm and nostalgic about raffling off Thatcher's clothes as if she were part of our glorious and patriotic narrative. When a substantial collection of Churchill memorabilia came up for auction in 2010, one of his cigars went for almost £600,000. The buyer presumably failed to remember – or didn't like to dwell on – the fact that the jaws clamped around the world's most expensive stogie once spoke out against the creation of the NHS.

A stand-up show in London tonight celebrates Margaret Thatcher, performed by comedians, such as Arthur Smith, who say they owe their success to her. Where would their careers have been without her to ridicule? Thatcher is more than the sum of her wardrobe; she is a cultural phenomenon. These are not just suits: they belong in glass cases, like Lenin's head, to remind us. And to warn us.

Thatcher-bashing might be obvious; it might even be a little adolescent. But while these suits, in all their bright shades of peach and green, may be empty now, they're still full of meaning.

Twitter: @harrywalker1