Well, enough people have posed the question (and I didn't know the answer either) so I've done some research and according to the .gov website:
The police have the right (under the Police and Criminal Evidence Act, or PACE) to:
- take photographs of you
- take fingerprints
- take a DNA sample, such as from a mouth swab or head hair root
- swab the skin surface of your hands and arms
They do not need your permission to do this.
The police need both your permission and the authority of a senior police officer to take samples like blood or urine, or to take dental impressions. (This does not apply when they take a blood or urine sample in connection with drink or drug driving.)
So, there we have it - she's allowed, by law, to refuse.