Home Secretary Theresa May is due to set out measures to tackle extremism after recommendations from a taskforce set up by the prime minister.
The cabinet-level group was set up after the death of Fusilier Lee Rigby.
Its recommendations include a consultation on legal powers to ban groups that preach hatred.
There is also a suggestion that people who attempt to spread extremist views should be treated like those who indulge in anti-social behaviour.
The taskforce has met six times since June to examine ways to challenge the dissemination of extremist views in schools, colleges, charities, Islamic centres and prisons.
Senior members of the cabinet, including the deputy prime minister, home secretary and education secretary, have been actively involved, says BBC political correspondent Iain Watson.
Following the release of the taskforce’s final report on Wednesday there will be a public consultation on some of its recommendations.
These include whether the Home Secretary should have new powers to ban groups which preach hatred – if that is what the police advise.
And the government will consult on whether people who attempt to spread extremist views should be banned from getting in touch with those who they are seeking to radicalise and whether they should be prevented from entering certain premises such as schools or colleges.
Prime Minister David Cameron has said the measures are not aimed simply at violent extremists but those who seek to radicalise others.
He added that ‘extremism is not something we should be afraid to address for fear of cultural sensitivities.’
Mr Cameron set up the taskforce in June following the killing of Fusilier Rigby in Woolwich, south-east London, in May.
Its recommendations also include:
* more support to areas with the “biggest integration challenges”, especially those where “extremism is a particular problem”
* looking at possible legislation to strengthen the powers of the Charity Commission
* working with internet companies to restrict access to terrorist material online that is hosted overseas but illegal under UK law
* improving the process for the public to report extremist content online
Mr Cameron said: “This summer we saw events that shocked the nation with the horrific killing of Drummer Lee Rigby in Woolwich and murder of Mohammed Saleem in Birmingham.
“These tragedies were a wake-up call for government and wider society to take action to confront extremism in all its forms, whether in our communities, schools, prisons, Islamic centres or universities.”
He added: “I have been absolutely clear that this is not something we should be afraid to address for fear of cultural sensitivities.
“We have already put in place some of the toughest terrorism prevention controls in the democratic world but we must work harder to defeat the radical views which lead some people to embrace violence.”
Mrs May will make a written statement responding to the taskforce’s proposals.
Michael Adebolajo, 28, and Michael Adebowale, 22, currently on trial at the Old Bailey, deny murdering Lee Rigby in Woolwich, south-east London, on 22 May.
Mohammed Saleem was stabbed to death in Small Heath, Birmingham, on 29 April, just yards from his home after attending prayers at his local mosque.
Ukrainian student Pavlo Lapshyn was jailed for at least 40 years for murdering 82-year-old Mr Saleem and plotting explosions near mosques.