Police are faced with the “wicked problem” of predicting which of the 40,000 people known to them could launch a terror attack, it has been claimed.
Sir Mark Rowley, a former head of UK counter-terrorism, made the comments in the wake of the Reading terror attack on Saturday, in which three people were stabbed to death.
A 25-year-old man, named in reports as Khairi Saadallah, was arrested on suspicion of murder following the knife attack in Forbury Gardens park.
He was later re-arrested under Section 41 of the Terrorism Act, which gives police the power to detain him without charge for up to 14 days.
One of the victims of the attack was named on Sunday as James Furlong, 36, a teacher described as having a “real sense of duty”.
A second victim, American Joe Ritchie-Bennett, was named on Monday.
Two other people injured in the attack remain in hospital, while one has now been discharged.
On Monday, Sir Mark, former assistant commissioner for specialist operations in the Metropolitan Police, told BBC Radio 4’s Today programme: "What you end up with operationally is about, I think, about 3,000 people under investigation at one stage.”
He added: "But there is 40,000 people… whose names have touched the system.
"And in that 40,000 are lots of volatile people who dip in and out of interests in extreme ideology, and to spot one of those who is going to go from a casual interest into a determined attacker, which can happen in a matter of days, is the most wicked problem that the services face."
On Monday, security minister James Brokenshire told BBC Breakfast: “What I would say is that the police and security services obviously deal with thousands of leads, that they have difficult challenges that they have in terms of prioritisation of resource.
Watch the video below
“But I can assure that if there are lessons to be learned, there are policies that needs to be changed, if we need to do things differently, absolutely that is what we will do."
Brokenshire said police and security services have prevented 25 attempted terrorist attacks in the past three years.
The Press Association reported that Saadallah, a refugee of the civil war in Libya, came to the attention of MI5 last year, but the information provided did not meet the threshold of investigation.
PA reported that MI5 received intelligence he planned to travel abroad, possibly for terrorism purposes, but the threat was found to be insubstantial.
Police have said they are not looking for anyone else in connection with the attack.
Boris Johnson said he was "appalled and sickened" by the incident and that "we will not hesitate to take action" if there are lessons to be learned from the circumstances.
The suspect was jailed in October for a complex series of non-terror offences before his sentence was reduced to one of 17 months and 20 days' imprisonment in the Court of Appeal.
One of the appeal judges who gave the judgment in March, Mr Justice Goss, noted Saadallah's various mental health issues in reducing the sentence.
Saadallah was released from prison earlier this month, PA reported.
Tributes have been paid to Mr Furlong, head of history and government and politics at the Holt School in Wokingham.
His parents, Gary and Janet, said in a statement: "He was the best son, brother, uncle and partner you could wish for.
"We are thankful for the memories he gave us all. We will never forget him and he will live in our hearts forever."