It is not exactly the image of loose-limbed and playfully sexual beauty that we have come to expect from a Mario Testino photograph. This new portrait of Baroness Thatcher, shot for Vogue in the Brook Penthouse at Claridges, looks alarmingly rigid.

Lady Thatcher stands in front of what appears to be a pile of mattresses, her hands clasped defensively in front of her, determined to stare down the camera. The royal blue dress, the brooch and pearls are resolutely anti-fashion and her helmet of hair, styled by Paul Allen, has been inflated into a formidable sphere, every hair smoothed into submission. Just like the Queen, Lady Thatcher's immaculate appearance still has a way of signalling the unassailability, longevity and immutability of her reign.

It is not easy to imagine the occasion. When photographing lithe young things, Testino, tall and tanned with big white teeth and wide eyes, tends to dance around theatrically with his camera, shouting “Wow! Amazing!” and “Work it! Work it!” with hot blooded, Latino passion. Convention dictates that this be met with a stream of ironic supermodel babble “Yeah, baby! Oh, baby, yeah ..!” and the look of having more fun than anybody else in the room. Lady Thatcher, on the other hand, looks as if she has not smiled in a hundred years.

Testino is not exactly insincere, he is just immensely hammy, and when in action on a shoot he crosses the line into a kind of hypnotic flattery.

When Lady Thatcher emerged for one of the shots in a pale blue shift dress and jacket, Testino (a man who knows what he likes in womanly chic) obliged her with his approval: “A perfect mixture of practicality and style,” he told her. His English is comfortably idiomatic but heavily accented and one can begin to imagine how the two of them, she 82 and he 53, embarked on a descent into treacly mutual appreciation. "Looks rather nice, though, doesn't it?,” commented Lady Thatcher when she saw the initial images. “I love the way you're such a perfectionist,” Testino beamed back at her.

Testino's studio in Paris is paid to edit and enhance until perfection is achieved in his pictures. Lady Thatcher's photographs will have been laid beneath transparent paper where a flurry of red dots will have alerted the retouchers to the flaws underneath.

Smoothed away, she looks out at us as indomitable as ever, an unmoving sculpture, and a very new kind of Testino woman.

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