Stores in most developed countries, UK included, can refuse service only for legitimate reasons, and they have to do so uniformly based on fair and unbiased rules. If they don't, they're at risk of an unlawful discrimination suite.
She didn't do anything that would be considered a "legitimate reason", and although applied uniformly, it's difficult to prove that an AI model doesn't discriminate against protected groups. Especially with so many studies showing the opposite.
I think she has as much standing as anyone to sue for discrimination. There was no legitimate reason to refuse service, AI models famously discriminate against women and minorities, especially when it comes to "lower class" criminal behavior like shoplifting.