What's the right way for UK Muslims to persuade extremists to stop being extremists?

There are certain people and a certain organization in the UK that (from what I've been told here) don't have grassroots support from UK Muslims on the whole. They do have support from the UK government, but it's not getting much traction from the broader Muslim community, specifically most of the people on this forum.

So. Without naming names or engaging in ad hominem attacks on people that I went out of my way Not to name, I have a couple of questions about where you are at.

Question one. On several occasions, I have seen the term "government stooge" repeatedly used, along with statements to the effect that some Muslims just repeat what the UK government wants them to say about extremism. Please read this question carefully and actually answer it, because this is the thing that I need an answer to. What exactly is the UK government saying about extremism, and what exactly is wrong with it?

Question two. Suppose a Muslim used to be an extremist, but now he's not, and what he now does is convince other people to take the same path of leaving extremism. If this were done in a forum-approved, truly grassroots manner, what would that look like? What would be the primary arguments against extremism, and in the end, would the newly-minted non-extremist seek to protect the lives of apostates, gay people, offensive cartoonists, Salman Rushdie, etc.?

Question three. As far as you're able to tell, is there any sort of proper grassroots desire among UK Muslims to get extremists to stop being extremists? If that's not the case, what do the grassroots want instead of that?