Unfortunately, copyright protection doesn’t extend that far. AI training is almost certainly fair use if it is copying at all. Styles and the like cannot be copyrighted, so even if an AI creates a work in the style of someone else, it is extremely unlikely that the output would be so similar as to be in violation of copyright. Though I do feel that it is unethical to intentionally try to reproduce someone’s style, especially if you’re doing it for commercial gain. But that is not illegal unless you try to say that you are that artist.
https://www.eff.org/deeplinks/2023/04/how-we-think-about-copyright-and-ai-art-0
True, I wrote this from a US law perspective, where that kind of behavior is expressly protected. US law is also written specifically to protect things like search engines and aggregators to prevent services like Google from getting sued for their blurbs, but it’s likely also a defense for AI.
Regardless of if it should be illegal or not, I feel that AI training and use is currently legal under current US law. And as a US company, dragging OpenAI to UK courts and extracting payment from them would be difficult for all but the most monied artists.