I don't know what she was saying to upset the crowd and neither do you. If she was saying that Muslims are all going to hell because of what's in the Qu'ran then I imagine some of them would get pretty upset. But I don't know.
For our purposes - at least the interesting side of this, I think - we can assume she says things that get Muslims very upset, things that we wouldn't say, yet are within the law to say.
Is it an arrestable offence to shout "string her up" from the crowd? At that stage would that person automatically become a criminal and be subject to arrest and incarceration? Because that's not what your link says. It specifies that the threat has to be in danger of being acted upon before it breaks the law.
Context is everything. "String her up" from a relatively jovial crowd, no problem, clearly not a real threat and nobody is likely to think that it was. Rather different if the mood is angry. The end of the clause specifies "
or whereby that person is likely to believe that such violence will be used or it is likely that such violence will be provoked". 'That person' could be either the target or another person, e.g. the police. So "String her up" followed by affirmation from others in an angry crowd could well be viewed as provoking the likelihood of violence, in context.
The word 'likely' is key to allowing the police to use a fair amount of discretion on how they respond, but it seems clear that the police did deem violence likely. In such a situation, I'd say that zero tolerance of actual verbal threats would be the correct response (although I can imagine circumstances might not allow it).
Let's agree that she should be protected from violence and that this is the police's job. How should they go about this? Should they fence off the platform? Keep a watchful eye on the crowd to make sure nobody says something out of line? I'm sorry if these seem like strawmen to you but I genuinely don't know how they should approach this.
The accusation is that the police have washed their hands of this situation and are putting her in danger. I'd like to know how they go about rectifying this without heavy handedly stamping on everyone's right to boo her or disagree verbally.
You've got to admit it's something of a strawman when you diminish "verbal threat of violence" to "says something out of line". Legally, there is a clear definition of the former. I'm using that term deliberately to identify the action that's unacceptable (with no implication that any are guilty of it, just with the background that we know the police thought there was a threat).
In practical terms though you're right, there's no obvious easy answer. But removing the speaker (either by force or persuasion) is certainly
not the right course of action, particularly in the message it sends to those who were threatening her - that intimidation and threats can get you what you want.
What's wrong with keeping a watchful eye on the crowd? After all, the police are mainly there because of the protest, not because of the speaker. And if there are people making threats that seem serious enough to worry them, then they should act on those individuals. None of that impinges on anyone's right to peaceful protest, booing, or other non-threatening forms of dissent.