To prevent any such temptation, we must be clear in our heads that there is no sense whatever in blaming Islam, a religion that gives consolation and enrichment to the lives of hundreds of millions of peaceful people.
So we need to make a hard and sharp distinction between that religion - and the virus of "Islamism". This is a sinister political agenda that promotes a sense of grievance and victimhood among a minority of Muslims. The Islamists want universal sharia law, and other mumbo jumbo. Above all, they want power over others: and so they prey on young men who feel in some way rejected by society, and they fill those young men with a horrible and deluded sense of self-importance. They tell these people that they are not alone in suffering injustice; that they belong to a much wider group of victims - the Muslims - and that the only way to avenge these injustices is jihad. These Islamist evangelists have no allegiance to the Western society they live in and whose benefits systems they abuse: far from it - their avowed intent is to create a sexist and homophobic Muslim caliphate.
You cannot hope to solve the problem of Islamism by accepting their invitation to enter into some debate or discussion about British or American foreign policy, even if that were desirable. People who suggest as much are, alas, playing the game of the Islamists. The only realistic option is to try to help immunise the vast, innocent and law-abiding majority of the Muslim population from the virus of extremism, and at the same time to try to stamp out that virus.
It is very important not to exaggerate the plague. It is hard to estimate the number of people who have succumbed to the Islamist virus in this country, and there are various degrees of infection. But the security services would probably put the number in the very low thousands; and when you consider that there are about a million Muslims in London alone, you can see how the reputation of a whole community is at risk of suffering from the actions of a tiny, tiny fraction.
But it is also vital not to be complacent, and to understand that the security services do an extraordinary job of dealing with a problem that has proved tough to eradicate. There remains a hardcore of activists and agitators, many of whom were associated with the now-banned organisation al-Muhajiroun. They cause real difficulties for mosques in London, some of which have had to resort to long and expensive legal actions to keep them out. The vectors of the virus may not even make much physical contact with their targets: since the arrival of the internet, we have had to deal with miserable young people "self-radicalising" - simply by watching sermons and other material on the web.
We need to recognise, loudly and publicly, the good work of the vast majority of Muslim organisations in helping to crush the problem. If they are going to show zero tolerance of Islamism, they need support and encouragement.
We need to keep on with the work of the "Prevent" programme, an initiative aimed at catching the most vulnerable young Muslims, and helping them before they can contract the virus. Prevent has recently been reviewed so as to focus its efforts on stopping the bad guys from recruiting, rather than just giving cash, in a general way, to Muslim community groups. But in some London boroughs there is clear and encouraging evidence that these programmes are working - saving young people from the catastrophe of being brainwashed by the Islamists. We need to keep immunising where we can, and we need to stamp out the virus.
People like Abu Qatada should be put on a plane, and those who preach hate and violence must be arrested. The universities need to be much, much tougher in their monitoring of Islamic societies. It is utterly wrong to have segregated meetings in a state-funded centre of learning. If visiting speakers start some Islamist schtick - and seek either to call for or justify violence - then the authorities need to summon the police.
The police need all the assistance they can get. The officers who attended the crime last week showed exemplary coolness and courage, and it is a fine irony that one of the firearms squad who helped to immobilise the alleged killers was a WPC: a fitting rebuttal of the ghastly sexism of the Islamist ideology. I have no idea whether the police would have benefited, in the Woolwich case, from the powers they now seek under the Communication of Data Act. But I have much sympathy with their basic desire to keep up with criminals, and make use of technology that is now instrumental in solving thousands of crimes.
That is how we are going to prevail in this struggle: by keeping our heads, by not falling for the tricks of those who want to provoke us, and by coming down hard when needed. We know we will win, and they know it, too.
Boris Johnson is the mayor of London.
