PERHAPS we underestimate her.

Perhaps familiarity – all those years, all those Brit Award nominations – has bred a kind of indifference. We see Annie Lennox, but do we really notice her any more?

While the media go wild over the arrival of the Bowie exhibition at the V&A this month, there's much less interest in the arrival in Edinburgh of an exhibition about the image of Annie Lennox. Of course, you might say that's because it's already been seen in London. And that's true enough, but then there wasn't much of a song and dance about it when it opened there either.

So let's take the arrival of The House Of Annie Lennox at the Scottish National Portrait Gallery this weekend as an opportunity to reassess a talent that's too easily written off as a great voice and little more. Lennox may not have changed the world in the way that Bowie did – and he did – but more than most she managed to question pop's default notions of identity and gender in the early days of the Eurythmics.

And it's all the more remarkable given that there was no evidence that it was coming. As the frontwoman of the Tourists, she didn't have the confidence or inclination – or the money, to be honest – to challenge our ideas of how women should look. But when she reconvened with her former lover Dave Stewart on a new musical vehicle, the Eurythmics, in 1980, she overhauled her music and her image. She cut her hair, donned a suit and tapped into pop's early-1980s' fascination with androgyny and gender fluidity, a fascination that could be also be seen in everyone from Boy George to Grace Jones.

"I wanted to see if I could get rid of the woman completely, and killed Annie of the Tourists stone dead," she told music journalist Lucy O'Brien. "I knew it would cause a few raised eyebrows. There's something subversive about it that I enjoy."

That sense of play was on display in the then new artform of the pop video that accompanied the singles from the Sweet Dreams album. It's difficult now perhaps to recognise how subversive she was being back then.

In 1984, O'Brien points out in her book, She-Bop, MTV were so nervous about Lennox's appearance at the Grammy Awards that they demanded to see her birth certificate. As a result, she "manned up" for the show, coming on as Elvis with fake sideburns and slicked- back black hair.

In the years that followed she played with a number of images of femininity. Perhaps it didn't have the same impact because it was about messing around with more traditional ideas of female presentation. Perhaps it was because the music was more mainstream, tapping in to the ersatz Motown vibe of the time (mainstream is one description, others are less kind. "Self-satisfied, lazy and sickly beige" is music journalist Garry Mulholland's summation of the Eurythmics' mid-1980s period).

But that blanket dismissal rather overlooks the music and image of the band's sixth album, Savage, in 1987, a chillier offering which saw Lennox playing with images of male transvestism in the accompanying videos.

If her solo years never quite ventured so far, she was still playing around with theatricality (very Bowie) and gender in her appearance until the 2003 release of her album, Bare, at least.

But that was 10 years ago and perhaps in the past decade we have forgotten quite how radical Annie Lennox could be.

And then you talk to her peers and performers who weren't even born when she was in her prime and you realise that they at least were paying attention all along.