Not in the UK, but I once organized a protest. I talked to the police beforehand. Their questions were very interesting: "Where? When? How many people? Will you have signs? Will the signs be on poles? What will the poles be made out of, and how thick will they be?" They didn't care about the act of protest, or about the content of the protest. They cared about the potential for sign poles to be used as clubs - about the potential for it to turn violent.
I must say, I think that's legitimately a concern for the police.
I'm sure 90%+ cases are legitimate concerns and even handed enforcement.
The issue is the legislation doesn't specify those things and just allows control of protests for basically any reason at the discretion of the police.
The police are not equipped to make those societal decisions IMHO, and the legislation is far far too loose.
Incidentally, the times when the legislation is abused tends to be the times when it matters greatly that it isn't.
I must say, I think that's legitimately a concern for the police.