Tony Blair warned today of the "long and deep struggle" against terrorism as the head of MI5 issued a stark assessment of the danger posed by al-Qa'ida.
The Prime Minister backed a speech by Dame Eliza Manningham-Buller in which she said the threat would "be with us for a generation".
Mr Blair said Britain must "stand up and be counted" to tackle the "poisonous propaganda" warping young people's minds.
In her speech yesterday, Dame Eliza said young teenagers were being groomed as suicide bombers.
She also said security services were aware of around 30 plots to "kill people and to damage our economy", targeting 200 groups and more than 1,600 individuals who were actively involved.
They had managed to thwart "five major conspiracies" in the UK since the July 7 attacks that threatened hundreds and possibly thousands of lives, Dame Eliza said.
Mr Blair, speaking at a Downing Street press conference today, said: "I have been saying for several years this terror threat is very real. It has been building up over a long period of time."
He added: "I think she's absolutely right that it will last a generation.
"We need to combat the poisonous propaganda of those people that warps and perverts the minds of younger people.
"It's a very long and deep struggle but we have to stand up and be counted for what we believe in and take the fight to those people who want to entice young people into something wicked and violent but utterly futile."
Mr Blair added: "This is a threat that has grown up over a generation.
"In the end the values we have and hold dear in this country are the values that will defeat those values of hatred, division and sectarianism."
Muslim Labour MP Shahid Malik said of Dame Eliza's speech: "It clearly tells us the size of the challenges that exist in our society.
"It means that certainly we have got to remain vigilant - it is an ongoing threat - but obviously you are more likely to be injured in a road accident than you are through a terror attack. We must remain alert but not overly alarmed."
He rejected the suggestions that Dame Eliza's assessment stigmatised the Muslim community as a whole.
Mr Malik said: "The people that stigmatised the Muslim community were the bombers on July 7 and Muslim groups need to wake up to that. That is what started this stigmatisation process."
Meanwhile the Muslim Council of Britain described the speech as a " sobering" warning and said it would be "prudent to assume that there are cells out there plotting similar outrages".
Spokesman Inayat Bunglawala repeated calls for a public inquiry into the July 7 attacks to find out the reasons behind young people turning to extremism.
In her speech at Queen Mary's College, London, Dame Eliza warned that radical elements in the UK were grooming young teenagers to become suicide bombers.
She said: "My officers and the police are working to contend with some 200 groupings or networks, totalling over 1,600 identified individuals (and there will be many we don't know) who are actively engaged in plotting, or facilitating, terrorist acts here and overseas.
"The extremists are motivated by a sense of grievance and injustice driven by their interpretation of the history between the West and the Muslim world."
This view was shared by a "far wider constituency", she said, adding that if opinion polls since last July's attacks were "only broadly accurate", more than 100,000 UK citizens believed that the July 7 attacks in London were justified.
"More and more people are moving from passive sympathy towards active terrorism through being radicalised or indoctrinated by friends, families, in organised training events here and overseas, by images on television, through chat rooms and websites on the internet," Dame Eliza said.
Al Qaida's "sophisticated propaganda machine" meant that attacks in Iraq were videoed and posted on the internet within half an hour, and later packaged "for a worldwide audience".
"Chillingly, we see the results here. Young teenagers being groomed to be suicide bombers," she said.
Dame Eliza said: "Radicalising elements within communities are trying to exploit grievances for terrorist purposes. It is the youth who are being actively targeted, groomed, radicalised and set on a path that frighteningly quickly could end in their involvement in mass murder of their fellow UK citizens, or their early death in a suicide attack or on a foreign battlefield."
She added: "What we see at the extreme end of the spectrum are resilient networks, some directed from al Qaida in Pakistan, some more loosely inspired by it, planning attacks including mass casualty suicide attacks in the UK."
Home-made improvised explosive devices used today may be succeeded in the future by chemicals, bacteriological agents, radioactive materials and even nuclear technology, she warned.
"These plots often have links back to al Qaida in Pakistan and through those links al Qaida gives guidance and training to its largely British foot soldiers here on an extensive and growing scale," Dame Eliza said.
The task was "daunting", with an 80% increase in casework since January.
"We recognise we shall have scarce sympathy if we are unable to prevent one of our targets committing an atrocity."
Dame Eliza added: "I do not speak in this way to alarm (nor as the cynics might claim to enhance the reputation of my organisation) but to give the most frank account I can of the al Qaida threat to the UK.
"That threat is serious, is growing and will, I believe, be with us for a generation. It is a sustained campaign, not a series of isolated incidents. It aims to wear down our will to resist."
Massoud Shadjareh, chairman of the Islamic Human Rights Commission, claimed Dame Eliza's figures were contradicted by the small number of people who had been convicted of terrorism.
He said: "Although we recognise that there is a real threat, the suggestion that we could even face a nuclear threat will only contribute to paranoia rather than safety and security."Reuse content