* Cameron under pressure over Muslim schools report
* Issues of British identity, culture worry some voters
* Cameron promises 'muscular' action
By Andrew Osborn
LONDON, June 15 (Reuters) - Prime Minister David Cameron said on Sunday Britain had been too tolerant of Islamist radicalism in the past and allowed violent rhetoric to flourish, pledging a "muscular" approach to combat the problem.
Facing re-election next year, Cameron's tougher line comes days after the chief schools inspector said a culture of "fear and intimidation" existed in some schools due to what parts of the media called a Muslim extremist plot.
The findings, which included evidence of faith and gender segregation and funding misuse, caused tensions in Cameron's coalition government, with two of his most prominent ministers in a public spat about the authorities' response to the issue.
Questions about British identity have shot up the political agenda, with immigration joining the economy at the top of voter concerns for the first time in years. The UK Independence Party (UKIP), which has promised to sharply restrict it, won European elections last month, pushing Cameron's Conservatives into third place.
Writing in the right-wing Mail on Sunday newspaper, Cameron suggested that Britain had sometimes allowed unacceptable views to go unchallenged, in the name of liberalism.
"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," he wrote.
"This has not just led to division, it has also allowed extremism - of both the violent and non-violent kind - to flourish."
In February, a court sentenced two British Muslim converts to life in prison for hacking a soldier to death on a London street, a killing that provoked an anti-Islamic backlash.
Government sources say hundreds of young British Muslim men are also fighting in Syria, a worry for the security services who fear they will return home to spread extremism and possibly violence.
Cameron said it was time for Britain to take a more "muscular" line on what he termed extremism and to push "British values" such as tolerance and the rule of law more assertively, especially in schools.
The government was making sure new immigrants spoke English, said Cameron, and was returning to what he called "narrative history" to teach children about democracy and government.
His office said he had all kinds of extremism in mind not just Islamist radicalism.
Some British Muslims have rejected the inspector's report about several schools in the city of Birmingham which found evidence of a drive to impose Muslim cultural norms.
The Muslim Council of Britain, an advocacy group that aims to represent the interests of the 2.7 million-strong community, questioned the criteria used to inspect the schools and said: "There is a strong fear that these reports will be considered the results of a witch-hunt." (Editing by Robin Pomeroy)