Cameron, in a powerful intervention clearly aimed at "preachers of hate", said in an article in Sunday Mail that the failure to stand up to such firebrands has "allowed extremism 'both the violent and non-violent kind' to flourish".
It is time to stop being "squeamish about Britishness" and tell everyone who lives here that refusing to accept British laws and the British way of life is "not an option", he said.
Downing Street stressed that the prime minister's comments are aimed at all sections of the community, not just Muslims. However, they appear to signal a key change in the stance of successive recent governments, Tory and Labour, on this sensitive issue.
They have faced claims that some unrepresentative ethnic minority leaders have been given free rein to promote extremist views and trample on British laws and rights on democracy, women's equality, religious freedom and tolerance.
Cameron's initiative is a direct response to the 'Trojan Horse' scandal of Islamist extremists who infiltrated state schools.
School inspectors said that at some Muslim-dominated schools in Birmingham, pupils were taught that white women were "prostitutes", boys and girls were segregated, Christmas events were scrapped, tombolas were banned as "non-Islamic" and children in biology lessons were told that the theory of evolution was untrue.
The dispute convinced Cameron that it was time to lead a fightback on behalf of British values.
In addition, there are growing fears that radical preachers are encouraging young British Muslims to join terrorists fighting to bring down the democratically elected government of Iraq, says the article.
It is alleged that radical clerics have tried to establish "Sharia Law Zones" in some British cities, banning alcohol, gambling, and even music.