"Terrorists are methodically and intentionally targeting young people and children in this country," Evans said, according to text of his remarks delivered in Manchester, England. "They are radicalizing, indoctrinating and grooming young, vulnerable people to carry out acts of terrorism."
"This year, we have seen individuals as young as 15 and 16 implicated in terrorist-related activity," he said.
Evans' remarks before a newspaper editors' conference were his first public speech since becoming director-general of MI5.
His predecessor, Eliza Manningham-Buller, warned in a speech in November 2006 that her agents were tracking around 30 terror plots and keeping 1,600 suspects under surveillance.
"That figure today would be at least 2,000," Evans said.
The growth is partly down to better coverage of extremist networks, but "also because there remains a steady flow of new recruits to the extremist cause," he said.
The uncomfortable truth is attacks attempted against Britain "are not simply random plots by disparate and fragmented groups," Evans said.
"The majority of these attacks, successful or otherwise, have taken place because al-Qaida has a clear determination to mount terrorist attacks against the United Kingdom," he said.
But he warned efforts to tackle terrorism are being stalled by work to halt foreign intelligence agents from stealing sensitive information on civilian and military technology. He singled out agents from Russia and China for espionage activities.
"It is a matter of some disappointment to me that I still have to devote significant amounts of equipment, money and staff to countering this threat," Evans said.
Evans warned that plots in the last 12 months, including failed bomb attacks on London and Glasgow this summer, were increasingly being driven from overseas.
Testimony from a U.S. terrorist-turned-witness in British court cases has revealed how young Britons are trained for attacks at terrorist camps in tribal areas of Pakistan.
Evans said that though Pakistan remains a key training ground for Britons, similar centers are emerging elsewhere.
Al-Qaida in Iraq is attempting to stage attacks outside Iraq and parts of East Africa, particularly Somalia, have become a key area for training and planning of attacks on Britain, he said.
Terrorist activity is also increasing across Europe, Evans said, noting the recent arrests of suspects in Germany, Denmark and Austria.
Evans confirmed that by 2011, MI5's staff will more than have doubled in size to 4,000, up from 1,500 staff in 2001.
But he said work by his agents to thwart plots will not alone be enough to stop the threat of extremist terrorism, calling for greater efforts from the government and society to counter the message of radical preachers.
"If we only react tactically while our enemies plan strategically, we shall be hard put to win this. A key part of our strategy must be perseverance," Evans said. "It starts with rejection of the violent extremist ideology across society."