Extremism and division is flourishing in the UK because of a "worrying" failure to push British values, David Cameron said, as he set out plans to teach all school pupils about the Magna Carta.
Teachers were told by 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 they included "a belief in freedom, tolerance of others, accepting personal and social responsibility, respecting and upholding the rule of law".
Writing in the Mail on Sunday 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.
He also suggested that any move away from the "Western model" of democracy and free enterprise would threaten Britain's economic success.
With concerns high over more young Britons joining radical jihadists fighting in Syria and Iraq, he accepted that too much latitude had been allowed to opponents of democracy, equality and tolerance.
"In recent years we have been in danger of sending out a worrying message: that if you don't want to believe in democracy, that's fine; that if equality isn't your bag, don't worry about it; that if you're completely intolerant of others, we will still tolerate you.
"This has not just led to division, it has also allowed extremism - of both the violent and non-violent kind - to flourish," he said in the article.
"We need to be far more muscular in promoting British values and the institutions that uphold them.
"A genuinely liberal country believes in certain values, actively promotes them and says to its citizens: this is what defines us as a society."
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.
"As president Obama put it when he addressed MPs and peers in Parliament, 'What began on this island would inspire millions throughout the continent of Europe and across the world'."
Celebrations are planned next year to mark 800 years since King John signed the Magna Carta at Runnymede which established for the first time that the king was subject to the law.
Mr Cameron said they will now include lessons for all pupils.
"The remaining copies of that charter may have faded, but its principles shine as brightly as ever, and they paved the way for the democracy, the equality, the respect and the laws that make Britain, Britain.
"So I want to use this upcoming 800th anniversary as an opportunity for every child to learn about the Magna Carta, for towns to commemorate it, for events to celebrate it."
Mr Gove pledged "decisive action" after schools inspector Ofsted issued a damning verdict on the running of a number of Birmingham's schools.
Inspections conducted following claims of a takeover plot by hardline Muslims found that a "culture of fear and intimidation" has developed in some schools and, in several, governors exerted "inappropriate influence" over how they are being run.
A poll by Opinium for the Observer showed that 58% of voters believe faith schools should not receive taxpayer funding, or be closed altogether.
It found three quarters are concerned there is a serious risk pupils could be encouraged to adopt extremist views in predominantly Muslim schools.
Most, 56%, also thought all faith schools should not be allowed to teach only their own religion.
None of those which faced inspections over the "Trojan Horse" allegations were faith schools but shadow education secretary Tristram Hunt said he would like cross-party talks on the issue.
"Events in Birmingham have raised questions about faith, multiculturalism and state education and in the aftermath this is the moment to think about discussing, on a cross-party basis, how we manage potential tensions, particularly in urban districts," he told the newspaper.
He called for strong powers for Ofsted to inspect teaching of religion and backed the idea that schools should teach about other faiths.
British Humanist Association chief executive Andrew Copson said: "As things stand, 100% state funded "faith" schools can and typically do teach one religion as true and all others are false, while non-religious worldviews are often ignored entirely. They turn children away because their parents are of the 'wrong' religion or no religion, and they refuse to hire the best qualified staff for the same reason.
"The proportion of secondary-age pupils in religious state schools has gone up by 20% over the course of this century with no meaningful political debate of whether this is desirable, never mind about popular. That Tristram Hunt is now proposing to look again at some aspects of this system is to be welcomed."