I don't mean to be unhelpful, but what the legal position is is irrelevant. What you experience will be entirely at the discretion of any jobsworth you encounter, who may decide on the day that you are a terrorist or at least a terrorist sympathiser and give you a hard time and/or confiscate your film and/or your equipment. It's what
they think the legal position is that counts. You can assert your rights till you are blue in the face but it won't make any difference.
This has been the experience of people using mobile phones to film congestion and cock-ups at railway stations. Station staff told them it was illegal to film anything as it 'might assist terrorists'!
If I were doing it, I'd keep it discreet, and be prepared to be challenged, and stop immediately when challenged. If the first priority is to avoid aggro.