Teachers were told by Westminster Education Secretary Michael Gove that in the wake of the controversy over Islamist influence on some Birmingham schools they must in future "actively promote British values".
The Prime Minister said these included "a belief in freedom, tolerance of others, accepting personal and social responsibility, respecting and upholding the rule of law". He 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.
With concerns about young Britons joining radical jihadists, he said too much latitude had been allowed to opponents of democracy and tolerance.
Mr Cameron said it was "a matter of pride and patriotism" to promote British values and history and urged people to stop being "squeamish" about doing so.
He added: "I want to use this upcoming 800th anniversary as an opportunity for every child to learn about the Magna Carta."