"We need to be far more muscular in promoting British values and the institutions that uphold them," Cameron said as he backed education secretary Michael Gove's plans to put British values at the heart of the national curriculum.
Rejecting the moral relativism of some of his critics, he said: "A genuinely liberal country believes in certain values, actively promotes them and says to its citizens: this is what defines us as a society."
Writing in the Mail on Sunday, Cameron said they were "as British as the Union Flag, as football, as fish and chips" and it was "not an option" for anyone living in this country not to live by them.
"Of course, we should teach history with warts and all. But we should be proud of what Britain has done to defend freedom and develop these institutions - parliamentary democracy, a free press, the rule of law - that are so essential for people all over the world."
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He said that too much latitude had been allowed to opponents of democracy, equality and tolerance.
Cameron's comments came as authorities had found that "a culture of fear and intimidation has taken grip" at some Birmingham schools.
In the article he said that values including freedom, tolerance of others, accepting personal and social responsibility, and respecting and upholding the rule of law were not optional.
Cameron said "British values" included: "A belief in freedom, tolerance of others, accepting personal and social responsibility, respecting and upholding the rule of law."
He added that children from all backgrounds should be taught about the Magna Carta, saying the document established the rule of law and paved the way for parliamentary democracy.
Describing the document as "the foundation of all our laws and liberties", he said: "I want to use this anniversary as an opportunity for every child to learn about the Magna Carta, for towns to commemorate it, for events to celebrate it."
Cameron will host a reception at Downing Street tomorrow to launch a year of events to commemorate the charter's signing on June 15, 1215 at Runnymede.