Sir Paul Stephenson said it was vital that communities remained vigilant and urged members of the public to "trust their instincts" and report "any suspicious behaviour which may be terrorist-related".
"Vigilance should be our watchword," the Metropolitan Police commissioner added.
In his first speech since returning to work after surgery, Sir Paul said the "severe" threat from international terrorism was "not a bureaucratic description, but rather a factual assessment of the reality of the threat we face".
"To be blunt it means that an attack is highly likely and could occur without warning at any time.
"As Government, the police and the security service assess the impact and consequences of the death of Osama bin Laden, it is clear that there can be no let up in our vigilance."
Sir Paul said: "Osama bin Laden led an organisation which is responsible for the injury and death of thousands of people worldwide in the name of an extreme and perverted ideology, committed to the use of terror and murder to achieve their aims.
"However, one man's death does not mark the end of an ideology and we must remain alert to the continuing threat from al-Qa'ida, its affiliates and those acting alone.
"The police and security services will continue to work locally, nationally and with our international partners to do everything possible to counter the terrorist threat.
"But we cannot do this alone, we need the help of the public to protect the country from the threat of terrorism."
He went on: "All communities across the United Kingdom have a vital role to play.
"As they go about their daily business, whether work, leisure or otherwise, vigilance should be our watchword.
"My message is a simple one, public awareness can provide an essential edge.
"Members of the public should trust their instincts and engage with us, reporting any suspicious behaviour which may be terrorist-related."
Sir Paul also warned about the dangers of transferring counter-terrorism (CT) responsibilities from Scotland Yard to a new National Crime Agency.
"The CT infrastructure, integrated within local policing and communities, has enjoyed real success, is highly regarded worldwide and we should be careful only to dismantle it with good cause."
Delivering the John Creaney memorial lecture at the Policy Exchange think-tank in central London, he added: "We should be conscious of adding further complexity and of the effects on key intelligence relationships, by the creation of any additional organisational tiers within the counter-terrorism landscape.
"Perhaps of some relevance here are the conclusions of the "9/11 Commission Report" in the US when commenting on agencies' abilities to 'connect the dots"'.
Sir Paul also warned of the need to be careful of the timing of any debate of the UK's counter-terrorism structure.
"It is critically important that those discussions are timely, that we avoid any unnecessary distractions as both prepare for the Olympics and maintain our current level of operational activity, and that any conclusions are drawn on the best analysis and experience."
Sir Paul returned to work in time for last month's royal wedding after undergoing an emergency operation in January.
Surgeons successfully removed a pre-cancerous tumour from his femur in an operation before Christmas, but the growth caused further damage to the bone, which led to a fracture and a second "lengthy and complex" operation.
Linking counter-terrorism operations with serious and organised crime in a National Crime Agency could lead to tensions, Sir Paul said.
"We must be aware, as I most certainly am from my professional perspective, of the potential resourcing tensions of any organisational linking of counter-terrorism with serious and organised crime."
Sir Paul added he was "entirely comfortable" with Home Secretary Theresa May's position on the future of counter-terrorism operations.
He said his concerns over stripping away the Met's lead role in counter-terrorism operations were not a result of territorial self-interest.
"I, as Commissioner of the Met, can state quite unequivocally, that territorial and organisational self-interest would be deeply unattractive as a basis for both me, and many of my colleagues, for considering what should be the appropriate structures for responding to the terrorist threat we face.
"Frankly, I am proud we are better than that.
"National security is simply too important to be determined by such shallow motives, just as the protection of our citizens must be based on more than mere structural convenience."
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