I dont have high hopes, not because its Labour or any other angle, but because as a concept Prevent hasn't really worked.
There is a huge difference between an organised group with a set of beliefs trying to recruit new members, and open discussion (particularly SM) which then means some individuals take those ideas and often misuse them, because of their own personal issues (remember how many "terrorist" reports are characterised as "lone actors"). And also, if you feel alienated from society because of discrimination whether sexism, racism, and so on, and you start making loud declation saying how awful the state is, or the legal system or whatever, is that something that should be covered by Prevent. I can see, even without the trans agenda, many, many men saying that feminism is too extreme and anti men.
Secondly its just seem totaly hypocrasy. It was decided misogyny wouldn't be seen as hate speech, and now suddenly its so bad its going to be included in the Prevent programme?
What Prevent is, is basically an acknowledgement that society as a whole doesn't have the same influence on all people. So rather than looking at how society had failed, it says those who didn't respond are "bad" people and society will through Prevent re-educate them in a more hyper version that what transpires in a day to day way.
As suggested by PP, if misogyny is so awful why haven't politicians, the legal system, etc., done more to clamp down on it. Our whole culture is permeated by it, and if anything we live in a more sexist society. Have you ever seen a politician stand up and say anything about this. They can make emotional speeches about domestic violence, but never talk about why this happens. And at the same time they close women only services. NB this is NOT because of trans issues but because those taking the decision do a "cost benefit analysis" and because women have not value the analysis ignores their / our needs. (Its been in the news that yet another women's refuge that has been funded by the local council for decades will no longer be funded as it isn't a priority.) Dont ever forget the TRAs are partly as sucessful as they are because behind them are the for longer standing MRAs who now have an additional "legitimate" reason to say the sex class of women can be discriminated against.
Sorry that was a bit off topic, but to return to Prevent:
But its biggest flaw, as we know from the abuse of hate speech, organisations being Stonewalled, that it is based on people who are more than likely out of their depth to take decisions about how "bad" is this "bad" person.
Not saying this is the best analysis but article points out it is flawed from the start. If you substitute the word Muslim for gender critical women / girls it is a chilling idea. https://www.libertyhumanrights.org.uk/fundamental/prevent/