Meryl Streep's Margaret Thatcher reveals a modern icon | Alison Jackson

Meryl Streep portrays the former prime minister Margaret Thatcher for the biopic The Iron Lady. Photograph: Reuters

I wasn't the only one to be taken aback by the picture of Meryl Streep as Margaret Thatcher that was released this week, a publicity shot for Phyllida Lloyd's forthcoming biopic The Iron Lady. The picture stared at us from the front page of no fewer than five national newspapers. But what is it about this photograph that makes it so iconic?

The Iron LadyProduction year: 2011Country: UKDirectors: Phyllida LloydCast: Jim Broadbent, Meryl Streep, Olivia Coleman, Richard E GrantMore on this film

As an artist who has spent a lot of time setting up people to look like celebrities, including Thatcher, for my photographs and TV programmes, I can only applaud the casting: Streep is no Thatcher-lookalike, but she has the perfect nose structure for the job. The instant recognition is all in the make-up and styling, though. With that Queen Margaret-style bouffant, Thatcher had a hairstyle that was so old-fashioned, it's almost timeless. Tony Blair has had both flowing locks and a short crop, tanned and non-tanned features; Maggie's packaged look always remained the same.

François Mitterand described Thatcher as having the "eyes of Caligula, and the mouth of Marilyn Monroe", but her hair isn't unlike Monroe's either. That big, wavey quiff creates an outline that is almost the width of her shoulders. Compare it to Andy Warhol's pictures of Monroe, or even Alberto Korda's portrait of Che Guevara. The three of them couldn't be further apart ideologically, but they all had what it takes to become a modern icon: big hair, high foreheads and a face that would allow you to project your own fears and desires onto it.

I would go as far as saying that in terms of creating an iconic image, Thatcher's hair gave her an advantage over Churchill, who had the grumpy look and the cigar, but was mainly still focussed on his voice for projecting a public persona. Thatcher's image, on the other hand, was perfectly suited to the age of television.

The other thing that strikes you about the picture are Streep's eyes, and the mixed feelings they evoke. She's staring straight down the barrel of the camera, which is both sexually provocative and downright threatening. When she was in government, Thatcher's femininity was often downplayed – not least with her deep, masculine voice. But looking at this picture, you are reminded that there was also a sexual dimension to her persona. Look at those arched eyebrows: it makes it look as if she's following the photographer's every move, like a hawk.

These days, it's much more common for politicians in TV interviews to look at the interviewer to the side of the camera, creating a nice profile. To me, this always makes them come across weaker than they really are. I always remember a textbook TV interview with Bill Clinton from early 90s, in which he started by facing his audience while talking, but was looking straight at the lens by the time his speech was finished, making an entire nation in front of their TVs feel as if they were being addressed directly. Thatcher knew of the power of the camera, too, and always made sure she was in complete control of where photographers were positioned when she gave her speeches. She didn't like compromise – and this is definitely reflected in this photograph.

Is Streep going to change the way we remember Thatcher? Perhaps. This photograph and the film might well be part of a wider shift in the way we remember her governing years. The Maggie Thatcher of 2011 is the prime minister at her most powerful: the PM of the Falklands war, brimming with confidence, rather than the ousted leader leaving Downing Street in tears.

But there's also a warmth in this picture that we don't usually associate with her, emphasised by the yellow-ish hue of the background. Compare it with the Richard Stone portrait that was unveiled in Downing Street in 2009. Streep's Thatcher is ever so slightly leaning forward, as if she is keen to reach out to you. Is there even a hint of a smile?

Lloyd's film comes more than 30 years after Thatcher first came to power. All of our lives have been affected by the social changes brought about by her government, and our own careers shaped by her political beliefs. If nothing else, this picture might be a reminder of how it is harder these days to be critical of Thatcher without seeming hypocritical.