People in the UK should stop being "bashful" about being British, the prime minister has urged.
Writing in the Mail on Sunday, David Cameron said the country should be "far more muscular" in promoting its values and institutions.
He backed the promotion of "British values" in the classroom amid claims conservative Muslim governors had tried to influence some Birmingham schools.
This should include teaching children about Magna Carta, Mr Cameron said.
Mr Cameron wrote that in recent years, the UK had sent 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."
Education Secretary Michael Gove has promised "decisive action" after Ofsted inspectors said that in several schools in Birmingham, the governors had wielded "inappropriate influence".
Its report followed claims they had sought to influence the ethos and curriculum of schools in the city.
Culture Secretary Sajid Javid warned even a small number of people wielding their influence could have a "great impact".
"It's always a small minority that spoils it for everyone and although it's a small number they can have a great impact," he told the BBC's Andrew Marr Show.
"That's what we've seen in these schools - that's what we're potentially seeing with British people going over to fight in Syria, which I think is unacceptable."
Mr Javid said he supported the prime minister's plans to take "a more muscular attitude" to promoting British values in schools.
But he added that the "vast majority" of British Muslims were important parts of the community who played the same roles as others and had tolerance and respect for British values.
In the wake of Ofsted's findings, Mr Cameron said "British values" included: "A belief in freedom, tolerance of others, accepting personal and social responsibility, respecting and upholding the rule of law."
These were "as British as the Union Flag, as football, as fish and chips," he wrote in the newspaper article.
The Muslim Council of Britain said it had "deep concern at the tone and tenor over the debate on British values".
In a motion passed at its AGM, the MCB said it had "no objection to British values" and believed in a "tolerant, more free and more equal society".
But it said it wanted a "real debate that does not regard us as conditional Britons.... It is not Islam or Muslims that stand in the way of full participation; It is the active and vociferous campaign to exclude Muslims from the public space."
'Way to democracy'
In 2015 it will be 800 years since King John put his seal on the Magna Carta, the document which first established the king was subject to the law.
Mr Cameron said he wanted all pupils to take lessons on the charter to mark the anniversary.
"The remaining copies... may have faded," he wrote. "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."
Mr Cameron said he also wanted "towns to commemorate it [and] for events to celebrate it."