Had the terrorist plan to blow up five American airliners succeeded, the consequences would have been, as Scotland Yard said, “mass murder on an unimaginable scale”. At least 1,500 people could have been killed: men, women and children, Christians, Muslims and atheists, holidaymakers and businessmen, burnt and mutilated by pathological fanatics whose perverted idea of Muslim salvation prompts them, allegedly, to conspire at carnage.

The horror of what may have happened is matched only by the relief that this plot was thwarted. But although innocent lives have been spared, the consequences are as profound as those that followed the London bombings a year ago. Air travel, public security, religious tolerance, social harmony and national priorities — all will be affected.

After the London bombings, the police and security services gave numerous warnings that the terrorist threat had not diminished; that fanatics would try again to kill on a mass scale; and that in Muslim neighbourhoods zealots were still trying to recruit disaffected youths to the jihadist cause. But over the past year complacency has grown. The report on the London bombings highlighted mistakes that the security service should have avoided. The police have been unable to stem damaging detail on the shooting of Jean Charles de Menezes. The Forest Gate fiasco raised questions about the reliability of intelligence and the police response.

Cynicism has crept into the discussion, not least among Muslims, who mistakenly see themselves as the target of the campaign against terrorism and insist that Islamophobia has grown. Their disaffection has been fuelled by the war in Lebanon — political events clearly influence the extremist movement, but they do not define it.

Complacency ended yesterday. The scale of the plot, the number of arrests and the continuing investigations into a conspiracy that reached back into Pakistan as well as across the Atlantic show that the threat is acute. The call yesterday by both the police and by John Reid, the Home Secretary, for vigilance should need no reinforcement: as they pointed out, the public gathers the best intelligence. And the best reaction of any citizen determined to play a role in defeating terrorism is to remain alert, informed and watchful.

That message applies especially to the Muslim community. For the past year, British Muslims have been in a state of turmoil, profoundly shocked by the discovery that the London bombers were born and brought up in Britain: instead of integrating, they sought their identity in alienation. Most Muslim leaders have accepted offers by the Home Office, community leaders and other faith groups to help in reaching out to the young, the angry and the potentially violent.

A certain amount has been done, and some Muslim leaders have emerged from a paralysing state of denial to argue vigorously for a better understanding of their faith — by young Muslims as well as by outsiders. There have been welcome initiatives: task forces sent to Muslim communities to tackle extremism; programmes to ensure better training for imams; and a more concerted attempt to inculcate the duties of citizenship.

Nevertheless, it was dispiriting to find yesterday that several Muslim groups were openly sceptical, saying that the police had been trying to intimidate Muslims with earlier raids and accusing the Government of timing the latest arrests to distract attention from the criticisms of its stance on Lebanon. Such self-deception is extremely dangerous. Islam has an identity crisis that it must combat. A virulent strain that mixes testosterone and a nihilistic theology has afflicted a small minority of young Muslims.

There will also be critics and cynics who are not Muslim, who would like to believe that if only foreign policy would change, the threat would immediately recede and the extremism evaporate. Those who would commit mass murder are not to be appeased by this or that policy fluctuation. Jihadists see Western society as innately evil, an existential threat to their puritanical, obscurantist version of Islam. They cannot come to terms with sexual equality, Western values, tolerance or democracy. To them, the Palestinian or Iraqi contexts are only settings for the introduction of an ideology that is utterly intolerant and regards moderate Muslims as apostates. If policy on either changed, they would look for other justifications for their fanaticism.

Both the police and the Government yesterday had clearly drawn lessons from earlier terrorist emergencies, especially the de Menezes killing. They were swift to give clear statements on the arrests, while being careful not to speculate or prejudice future criminal trials and the continuing inquiry — which will be long and spread far wider. Already it has been made clear that Pakistan, from where many of those arrested or their families came, has been helping in the international surveillance of the suspects. If the public is to be convinced of the threat, accept temporary travel restrictions and not be unduly alarmed by the raising of the security alert, the police must provide as much accurate information as possible, as swiftly as possible. If there have been mistakes, they must be admitted, and if there are residual concerns, they must be explained.

It was revealed last week that Britain’s security services have foiled 13 terrorist plots. There are certainly others still being hatched. Defending Britain’s security is a costly, secret and often thankless task. But it is vital. And while the details of how this latest plot was thwarted may never be known, the public will be grateful that the intelligence services have, for now, proved up to their task. This is a long battle, in which the police and MI5 will be engaged for many years. They deserve all the backing that a vigilant public can give them.