By Michael Holden and Paul Sandle

LONDON (Reuters) - British Prime Minister David Cameron unveiled a new strategy on Monday to combat extremism, saying the battle was "perhaps the "defining one of this century", but his proposals were condemned by Muslims as demonizing their communities and set to fail.

The Counter-Extremism Strategy has been promised by Cameron's government for months, designed primarily to counter the ideology promoted by Islamic State militants, al Qaeda and other Islamists which the authorities say can lead young Britons onto a path of violence.

"Subversive, well-organized and sophisticated in their methods, Islamist extremists don’t just threaten our security, they jeopardize all that we’ve built together – our successful multi-racial, multi-faith democracy," Cameron wrote on his Facebook website.

"So we have to confront them wherever we find them."

British police arrested a record number of people last year on suspicion of terrorism offences, and say they have thwarted a growing number of plots hatched by young Britons, some of whom had been radicalized in just weeks via the Internet.

Earlier this month, a 15-year-old boy was jailed for life for inciting an attack on a World War One commemorative event in Australia from his bedroom in northern England.

Under the wide-ranging proposals, groups deemed extremist by promoting hatred will be banned; places where radicals thrive including mosques could be closed and the regulator Ofcom will get tougher powers to address TV and radio channels airing extremist material.

The new law would also give parents worried that their 16 and 17-year-old children might travel to join Islamic State the power to apply to have their passports removed, while anyone with a conviction for terrorist offences or extremist activity would be banned from working with children.

The plans are designed to target all hate groups, including far-right organizations, but they were met with immediate opposition from Islamic groups who variously described it as "war on Muslims" or containing "McCarthyist" undertones.

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The Muslim Council of Britain (MCB), the country's largest umbrella Islamic organization, said that while terrorism was a real threat, the government's strategy was based on poor analysis and risked alienating those whose support it needed.

"Whether it is in mosques, education or charities, the strategy will reinforce perceptions that all aspects of Muslim life must undergo a ‘compliance’ test to prove our loyalty to this country," said Shuja Shafi, the MCB's Secretary General.

Muslim groups are not alone in their scepticism. Some lawmakers in Cameron's own party are uneasy at the measures, while counter-extremism experts say the message of militants should be challenged not banned.

David Anderson, the independent reviewer of anti-terrorism legislation, has warned that any wrong decisions risked provoking a backlash in Muslim communities and driving people towards extremism and terrorism.

(Editing by Stephen Addison)