New Government legislation will include powers to put non-violent extremists who radicalise young people "out of action", David Cameron has said.
The action against Islamist "influencers" forms part of a five-year plan to crush the home-grown extremism which the Prime Minister said had led to up to 700 young Britons travelling abroad to fight for the Islamic State (IS) terror group and left Muslim parents "living in fear" that their children may be radicalised.
In a high-profile speech in Birmingham, Mr Cameron announced plans for a new scheme allowing parents to apply to have their own children's passports removed if they suspect them of planning to travel abroad to join a radical group.
The PM said Britain must act to "de-glamourise" groups like IS by making young people aware of the brutal reality of life in the parts of Iraq and Syria which they control.
And he said the UK should do more to promote its own creed of tolerance, democracy, the rule of law and freedom of speech and should make clear that the doctrine of respect for different faiths must be matched by those faiths supporting the British way of life.
Mr Cameron said it was not enough for extremists to say they opposed IS - also known as Isil, Isis or Daesh - for them to prove that they were not a threat. This would be setting the bar for acceptability "ludicrously low", and groups should be expected also to condemn conspiracy theories, anti-semitism and sectarianism, he said.
"We need to put out of action the key extremist influencers who are careful to operate just inside the law but who clearly detest British society and everything we stand for," said the Prime Minister.
"These people aren't just extremists, they are also despicable far-right groups too, and what links them all is their aim to groom young people and brainwash their minds.
"Let's be clear who benefits most from us being tough on these non-violent extremists - it's Muslim families living in fear that their children could be radicalised and run off to Syria, and communities worried about some poisonous far-right extremists planning to attack your mosque."
A new Extremism Bill will include "narrowly-targeted" powers to tackle these "facilitators and cult leaders" and stop them "peddling their hatred", said Mr Cameron.
He also said the Government would take action to tackle sectarian and communal segregation in schools, and called on communications watchdog Ofcom to clamp down on cable TV channels broadcasting extremist messages.
Universities should be ready to challenge extremist speakers on campus and broadcasters should use a wider range of speakers from Muslim communities, rather than repeatedly putting extreme voices on screen, he said.