In the case of the woman, I think its pretty clear cut.
Everyone in the UK has the right to (legally and peacefully) make a protest. Problem lies in the fact some protesters, like that daft woman, think that means that is also gives them the right to give the police a load of face. How is giving the police large, who are trying to maintain order, going to help their cause?
I thought I wouldn't say anymore on this subject..........but exactly right TB!!

Don't know enough about the woman incident really, but use of a batton is to protect an officer, colleagues and the public.
I doubt very much it is acceptable to use it to shut up a non violent, protestor that, from the little I have seen, made no aggressive advances towards the officer. Apparently until he had given her a back hander, she hadn't even noticed him in particular.
He gave no warning, just a back hander to the head and when she voiced her objection, he drew his batton and, again with no warning, struck her on the leg. What on earth was he thinking ?
The brief clip I have seen showed his actions to be perfectly natural and 2nd nature to him.
Giving it large, or put another way, voicing an opinion in a non violent or aggressive manner is peacefull protest, and is a legal right in this country.
I'm not certain, but I think this officer is also a member of the T.S.G.
The problem with these incidents is that in future officers are going to be treading on egg shells in these situations.
The uniformed thugs are making the work of level headed officers in a volatile situation even more difficult.