Not sure about the UK, but here in Germany it's not legal to film a person in public.

Of course it's a bit more complicated as in you can be in background shots and have no right to complain.
But as soon as you become the focus (which was the case in the situation) you need to get consent to film. Especially if you are doing it publicly (which a livestream anyone can watch is) and commercially (she probably gets money/incentives for her blog post).