Home Secretary John Reid has revealed that "at least four major plots" have been thwarted since the 7 July attacks in London last year.
Mr Reid also said the government believes the first al-Qaeda plot in the UK was in 2000 in Birmingham, preceding the war in Iraq and the 9/11 attacks.
Police are currently quizzing 23 people over an alleged plot to blow up planes.
Detectives are conducting a major search for evidence at woods near High Wycombe in Buckinghamshire.
The home secretary said he thought it was right to keep Britain at the highest possible level of terrorist alert.
But he acknowledged that the "terribly inconvenient regime" of restrictions imposed on carrying hand luggage was affecting airlines and the travelling public.
He said those limits were being reviewed but any new regime would still need to ensure safety.
"We think we have the main suspects in this particular plot. I have to be honest and say on the basis of what we know, there could be others out there ... so the threat of a terrorist attack in the UK is still very substantial," he told the BBC programme.
While the police and security forces were doing their job with 100% effort, he said: "We can never guarantee 100% success."
"This has been an ongoing threat, it is a chronic one and it is a severe one," he added.
Even if the threat level was reduced to "severe", Mr Reid said it was "highly likely there would be another terrorist attempt and that is one thing of which we can be sure."
Asked whether the four major plots he revealed could have caused a major loss of life, Mr Reid said: "In my view yes, on the information I have received."
The Home Secretary was also asked about a report in Sunday's Observer newspaper which said that "up to two dozen" terror investigations were operating across Britain.
Mr Reid said: "I'm not going to confirm an exact number but I wouldn't deny that that would indicate the number of major conspiracies that we are trying to look at.
"There would be more which are not at the centre of our considerations and there may be more that we don't know about at all."
Responding to questions on whether the government would once again push for a 90-day detention of terror suspects, the home secretary said the current situation did not represent "a good time" to look at such measures.
NEW THREAT LEVELS
Low - an attack is unlikely
Moderate - an attack is possible but not likely
Substantial - strong possibility of an attack
Severe - an attack is highly likely
Critical - an attack is expected imminently
But he said it was his own view that 90 days was what police required.
He was also asked his opinion on a letter written by a group of British Muslim leaders who believed the UK's foreign policy could be linked to the terror threat.
Mr Reid said such a belief was a "dreadful misjudgement that foreign policy of this country should be shaped in part, or in whole, under the threat of terrorism activity".
Shadow home secretary David Davis, speaking on Sky News, also criticised the letter.
"It (foreign policy) might be part of the catalyst, but to explain this is not to excuse it," he said.
"There are plenty of people with legitimate arguments with the government's foreign policy on Iraq, in Afghanistan in Lebanon and the Middle East but none of them take the stance of attempting to murder many thousands of their fellow citizens".