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SpaceX, and electric car maker Tesla Elon Musk at a past event. [Alain Jocard, AFP]

A British lawmaker has filed a case at London's High Court against Elon Musk's xAI after its Grok chatbot tool was used to create fake sexualised images of her, including in a bikini.

Jess Asato, of the ruling Labour Party, said she lodged the "High Court claim against xAI, the company behind Grok" on Wednesday.

Grok sparked a global outcry earlier this year for allowing users to create and share sexualised pictures of women.