Usually export controls are applied to stuff where some significant % is made in America so a few US based engineers could make the project export controllable.
Or in the case of ASML machines, any company you can pressure to comply with your policies either by restricting their access to the technology you control or politics between governments.
But do they want to start a game of chicken with Google? Doing it to Anthropic is one thing, they're much smaller and less B2C. But Google is far more powerful and likely to defend their UK/EU business because they're also fucked if they don't.