The last time I checked my privilege it was wedged somewhere behind the Habitat sofa. But at least I have some idea where it might be. The applause given to Lily Allen's new video Hard Out Here has made me both sad and angry. Are our expectations of anything vaguely feminist so low we can wave through a little exploitation? Some minstrelsy?

Allen is apparently having a go at the nasty sexism of the music industry. She is funny and that all-purpose word "feisty". She speaks for all women who have "baggy pussies" and bodies changed by birth, and the Robin Thicke haters. She has got a brain, balls, tits and babies. She really has it all.

This is just a pop video, not a policy document, and all kinds of women have cheered her on. Socking it to the man! I like Allen's voice and presence and mouthiness, but I don't like racism. Even tongue-in-cheek, hand-on-slapped-black-buttocks racism. In the video she walks away from her twerking dancers. She remains in charge. They don't. Maybe I have read it wrong. But what I see is the black female body, anonymous and sexualised, grinding away to make the rent. Maybe I should just overlook it. Silly pop culture, full of "bitches" and "hos", T and A, and Justin Bieber drawing pictures of monkeys in gold chains. It's just fun!

I missed the meeting where one had to choose between racism and sexism. While it is obvious that not every feminist statement can or has to represent all women, I naively thought we had reached the point where we did think we had to represent someone more than just privileged white women. Sure enough, I have been told that the video is ironic. Ah, irony! The dead-eyed, conservative and lazy substitute for critical thinking.

Allen herself says the whole thing is meant to be lighthearted, dealing "with objectification of women … It has nothing to do with race at all." The whole thing may have been more lighthearted if the dancers also walked off at the end. You know, using their brains as well as their bodies. But what do I know? I am way too old for Miley. Even my 12-year-old is way too old for Miley Cyrus. Twerking isn't a recent invention. Has anyone been to West Africa? Jamaica? New Orleans or Tottenham? Miley can do what she likes with her own body.

But it is the continual, unrelenting exploitation of the bodies of black women (and men) that cannot be ignored. Soon everyone will cry buckets in cinemas watching 12 Years a Slave because, you know, it wasn't nice. But if anyone bothers to think about how black bodies came to be in America and how they came to be nothing more than units of economic production, then maybe the phrase "shake your money maker" becomes a little less joyous.

The great crossover of hip-hop here and in the US to middle-class youth has been intriguing to watch. To a large extent youth culture has imbibed all kinds of black cultures. We might think that brings with it an actual shift in power, but no. Look around at any gatherings, in the tech industry, in the City, while Cameron tells us that austerity is not just for Christmas but for life, and you will be hard pushed to spot a black face.

We are not post-racism any more than we are post-feminism. This is the context into which this video falls: a white middle-class woman playing ringleader to anonymous black women. Maybe there is a knowing wink here I missed. But I haven't missed years of black women writing about how their bodies are used for white people to write their own scripts all over them.

For as Simone de Beauvoir said: "The body is not a thing, it is a situation: it is our grasp on the world and our sketch of our project." This is the situation. Whether the project is feminism or a way of selling a song. Our sketches matter. Who gets to be in charge of our bodies matters. So I am sorry but Allen cannot be the one to say this is nothing to do with race. Racism works precisely by denying the presence of race. The privilege is to not notice it.

Does liberal feminism expect so little that we lap up the crumbs from the table? That we say to women of colour: I am afraid your concerns are a bit humourless, we will sort out the race stuff later, and by the way where did you get your nails done? Well, it's just not good enough for this bitch.

As hard as it might be here, I still know it's a damn sight harder for some bitches than others.