I went to a busy, city-centre Wetherspoons recently and ordinary waiting-on staff were wearing body cameras. I don’t see how this would be any different. Nor do I see how it’s any different to someone having a dash cam or filming on a mobile phone.
The Wetherspoons staff are presumably wearing company issued cameras in the course of their employment. The OP is asking about wearing his own camera when he’s at work - so surely the difference is obvious?
I’d echo what’s been said upthread, it isn’t illegal to wear a privately owned body cam, but is certainly unlikely to he something any employer would tolerate someone doing off their own bat, so to speak, given the potential GDPR issues/vicarious liability.