I haven�t the faintest idea of the answer to your question. I imagine a combination of your friend�s contract of employment, general employment law and, of course, the overarching Human Rights legislation (if your friend works for public body) would provide the answer.
However, I should like to pose one of my own. Why is it, that in response to what, on the face of it, seems a perfectly reasonable and innocuous request, your friend is reaching for her law books? I assume she is not being asked to dress in a short skirt, stockings and suspenders. So why not just do what the employer wants? After all, she has to buy some clothes to wear to work. Why not just buy some which will suit her employer? It will make him or her happy, might just provide a better working atmosphere for your friend and generally make life just that bit more bearable.
Even if your friend is �legally� in the right to deny this request, and succeeds in getting her own way, does she really think this is a good basis upon which to build an employer/employee relationship? Does she think her working life will be very pleasant?
We all have to make concessions in our working lives and life is too short to worry about such things. Your friend should comply with her employer�s reasonable requests or move on!