More than half the people of Britain are strongly opposed to a mosque being built in their neighbourhood. Only a quarter of Britons feel positive towards Muslims, while more than a third report feeling "cool" towards them. These are the ominous results from the latest British Social Attitudes Survey. So is Britain anti-Muslim? Is there a place for Islam in British public life?

This magazine is proud of its secular, liberal heritage. Our interest in Islam and Muslims is not religious or theological. But it is clear that, politically and culturally, Islam matters, and on a range of global issues, from the so-called war on terror to the Middle East peace process to the future of Europe. Here in Britain, much of the debate over terrorism and extremism, as well as race, immigration and multiculturalism, revolves - rightly or wrongly - around Muslim communities.

Since 11 September 2001, and especially since the attacks in London on 7 July 2005, many Britons have come to fear their Muslim neighbours: they worry about the bearded young man with a backpack sitting next to them on the Tube. There is also a widespread lack of knowledge about the central tenets of the faith itself and the basic fabric of British Muslim life. Fear and ignorance are a toxic combination, and myths and misconceptions abound.

Contrary to popular opinion, polls show that the overwhelming majority of British Muslims are integrated, loyal, non-violent and eschew religious fanaticism (page 26). But the antics of a small cabal of British-born Muslim radicals - exemplified by the buffoonish Anjem Choudary and his Islam4UK group (now banned by the Home Office) - bring the entire Muslim community into disrepute in this country.

Yet publicity-seeking hotheads like Choudary have been aided and abetted by a sensationalist press that often conflates the actions of an angry minority with those of the peaceful majority. Islamophobia now seems rife - in the words of one conservative commentator, "prejudice against Islam . . . is Britain's last remaining socially respectable form of bigotry".

In 2008, researchers at Cardiff University revealed that more than two-thirds of the stories about Muslims published in the press since 2000 identified them either as a source of problems or as a threat - culturally, as well as in security terms. More than a quarter of the stories propagated the idea that Islam is dangerous, backward or irrational.

This relentlessly negative coverage of Muslims and Islam must end. The liberal left has always defended minorities in this country - be they Jewish, black or gay. Today, it is Muslims who are demonised and bear the brunt of racist attacks. "I try to imagine how I would feel if this rainstorm of headlines substituted the word 'Jew' for 'Muslim'," wrote one leading Jewish commentator, in the wake of the 2006 row over the niqab, or Islamic face veil. "I wouldn't just feel frightened, I would be looking for my passport."

No religion or community is beyond scrutiny. There is a debate to be had about the role of Islam in modern Britain. British Muslims find themselves at, or near, the bottom of various socio-economic indices: poverty, unemployment, literacy and life expectancy. But the American Muslim experience offers hope. Muslims in America are among the nation's brightest and best-adjusted minorities: in a Gallup poll, 41 per cent of American Muslims said they were "thriving". This figure drops to 7 per cent in the UK.

President Obama has appointed the pollster Dalia Mogahed, a veiled Muslim woman, as one of his advisers on inter-faith relations. Sheacknowledges (on page 32) that, as "corny as it may sound", she is proof of the "American dream". Is America's "melting pot" a better model for the integration of Muslims than Britain's multicultural experiment?

Or does secular, democratic India offer a better alternative? That is the argument of Ed Husain (on page 28), the former self-described "Islamist". Acknowledging the way in which many Muslims have been radicalised in recent years, he makes a bold case for reconciling a new form of political Islam with liberal democracy. Husain and Tariq Ramadan (on page 22) remind us that the strength of Islam has always been its ability to adapt to different circumstances and cultures.

Misunderstanding Muslims can only lead to further tensions and will make civic harmony impossible. This week, the magazine attempts to offer a more nuanced understanding of a range of contentious issues, in particular whether Islam is compatible with the values and principles of western liberal democracy. Meanwhile, British Muslims, alienated, frustrated and under siege, need our support.