Disappointing that a police officer allowed himself to be bullied like that tbh. Whilst I am all for respecting him for not letting his personal opinions being shared when working in a professional capacity he could quite easily have said:
"Sorry, sir but I am allowed by the policies of the Metropolitan Police to wear this band. If you have an issue with the edict then you can contact xyz on tel no 123. I am sure you understand I am here to work in a professional capacity not discuss things of a personal nature." - and not remove the band.
If he can't stand his ground then I can't imagine his fellow officers will be that impressed with him even if he uses the avoiding confrontation line. In my opinion to prevent incidents like the police should not really be wearing such armbands for this very reason.
And before someone jumps on me for saying that I've done my fair share of tours in that part of the world and am an active supporter of Help for Heroes. Not everyone is a fan of such causes though, especially in an area like that, and there is no need for personal expression in a professional capacity in my opinion.