Her remarks were posted on the MI5 website on Friday.
She said that Muslim extremists were plotting at least 30 major attacks in Britain and the threats might involve chemical and nuclear devices.
Britain suffered its worst peace-time attack in July last year when four British terrorists blew themselves up on London's transport network, killing 52 commuters and wounding hundreds.
“We are aware of numerous plots to kill people and damage our economy. What do I mean by numerous? Five? Ten? No, nearer 30 -- that we know of.”
She warned that young British Muslims were being groomed to become suicide bombers.
Dame Eliza's warning comes days after a British man was sentenced to 40 years in jail for planning a series of attacks.
“What we see at the extreme end of the spectrum are resilient networks, some directed from Al Qaeda in Pakistan, some more loosely inspired by it, planning attacks including mass casualty suicide attacks in the UK.”
She added that tomorrow’s threat might include the use of chemicals, bacteriological agents, radioactive materials and even nuclear technology.
“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,” said Dame Eliza.
"This is a threat that has grown up over a generation. I think she (Dame Eliza) is absolutely right in saying it will last a generation," Prime Minister Tony Blair told reporters, according to the Reuters news agency.
Mr Blair said it could only be combated by tough terrorism laws and fighting `poisonous propaganda’, influencing young people.
The MI5 director-general said: “The video wills of British suicide bombers make it clear that they are motivated by perceived worldwide and long-standing injustices against Muslims; an extreme and minority interpretation of Islam promoted by some preachers and people of influence; and their interpretation as anti-Muslim of UK foreign policy, in particular the UK's involvement in Iraq and Afghanistan.”