What would be grounds for arresting someone at the tube stations? Is it illegal in the UK for police to believe you intend to go a certain area based on how you exit the tube?
Same grounds as for arresting them anywhere else, more or less. I am not saying that the police should ban protests (and they generally don’t). I’m just talking about the practicalities of how they could go about doing it.
It's not about grounds to arrest them, it's about practicality.
If you need to arrest someone in London (someone who might be about to cause harm) then there's a very good chance they will go through a tube station, and they tend to have relatively few, easily controlled exits. Most tube stations have two or less.
A few high profile tube stations occasionally have armed police presence.
But I think the idea that face recognition is being used to suppress protest is pretty overcooked; apart from the utter silliness around the banning of Palestine Action, we have a solid right to protest and we do.
The main problem is London has far too few police officers, and it has a transport system that is under consistent terror threat.