People associate successful black people with having lighter skin, according to new research. A study from San Francisco State University found that high-flying African Americans were falsely remembered as being several shades lighter than they really are, and it concluded that our memories comply with stereotypical ideas that associate "whiter" skin with favourable characteristics.

If my daughter's experience is anything to go by, perhaps I shouldn't be surprised. My five-year-old could be a poster girl for post-racial Britain. She has honey-coloured skin and Leona Lewis-style corkscrew curls. Strangers stop me in the street to comment on her good looks. But since the age of three she has complained about her appearance. Her hair isn't straight enough. Her skin isn't pale enough. And white characters in books, she tells me, are "better" than characters with black, brown or beige skin.

If my daughter undertook the famous Clark doll experiment, in which children choose between a white and black doll, I'm sure she would, like those studied, name the white one the nicest, while the black doll would be the bad one.

The other day, she showed me an iPad image of a black dress-up doll. I asked her if the doll was nice. "No she's not nice," she said. I asked her why not. "OK, I'll make her a bit more lighter skinned first." She got to work tapping the screen. When she finished, the doll's skin was white. "Here, I made her nice," she said.

Black friends tell me their girls express similar thoughts too, about what constitutes niceness and beauty. Yet we've all given them multiracial books and toys and tell them regularly how gorgeous they are. It seems a battle must be fought against the powerful and pervasive message that a white western appearance is the way to go.

So how are the minds of children – and adults – being influenced, or rather infected? Perhaps we should consider the aspirational images around us.

It's true that mixed-heritage children like my daughter can often be seen promoting kids' clothing. And Beyoncé features regularly in TV commercials. But take away the cute kids and the celebrity plugs, and the incidence of run-of-the-mill aspirational images involving non-white people is low. Naomi Campbell herself brought attention to Victoria Beckham's 30-strong lineup for London Fashion Week, which included only one non-white model.

I decided to examine the recent autumn and winter clothing brochures around my home. High street brands Debenhams and Joules featured no adult models of colour, although the child models were a multiracial bunch. White Stuff, beloved by the middle-class mummy brigade, featured not a single model of colour. Neither did posh adult clothing company Toast. Or fitness-wear brand Sweaty Betty. Only Boden, which counts Samantha Cameron and Michelle Obama among its fans, included a broad spectrum of child and adult models. I emailed three of the companies to ask about the lack of colour.

White Stuff marketing director, John de Chane, couldn't show whether the ironically named company, which has more than 100 UK stores and outlets, had ever used a model of colour. However, he wrote, "we've identified our model selection criteria is a key issue for us to address, and … it's on our agenda to make a positive effort to be truly representative going forward." Yippee! In the year 2014, this 30-year-old brand may actually begin to use models who reflect the society we live in.

Jessica Seaton, director of Toast, replied that her 14-year-old company seeks out women or men "with intelligence and something special about them". She added that on "a couple of occasions" people of colour had been found who fitted this description. Is she really implying that black models simply aren't bright enough? I hope not. And she continued: "If we search for a mixed-race or coloured girl … the models are more overtly sexy, vampish and not at all right for the brand. It's difficult and somewhat depressing, but this is the situation we are faced with." I was stumped by the "sexy, vampish" observation. Are black models being forced into this stereotype (the kind that Lily Allen seemed to be unconsciously buying into in her video last year)? And if so, one can only assume this is because model agencies are only being asked for this kind of black woman, which leads to further questions about how widespread and deep-rooted racism is within the fashion industry.

An unnamed Sweaty Betty spokeswoman gave me a more forthright reply: "We have taken your feedback on board and will definitely try to have broader representation of ethnicities over the next few campaigns." The lack of bumbling was refreshing.

This week it was reported that a Nigerian entrepreneur is trying to counter children's stereotypes by launching a range of black dolls. And as my daughter matures she appears increasingly aware of the positive aspects of darker skin. But I'm not overjoyed about having my job as a parent frustrated. I think it's my turn to do some excluding. I'll be spending my money in future with forward-thinking companies only.