Three people were also hospitalised after a man wielding a 13cm knife went on the rampage in a park on Saturday, randomly stabbing people enjoying a sunny, summer evening.

A Western security source, speaking on condition of anonymity, told Reuters that the suspect was a 25-year-old Libyan called Khairi Saadallah.

Calling the incident terrorism, police said a 25-year-old had been arrested but they were not hunting others.

"What we saw here on Saturday evening in Reading was the actions of one lone individual," Home Secretary Priti Patel said on Monday.

The Philadelphia Inquirer said one of the dead was US citizen Joe Ritchie-Bennett, 39, who had lived in Britain for 15 years.

US ambassador Woody Johnson sent condolences to families of victims. "To our great sorrow, this includes an American citizen," he said on Twitter.

Teacher James Furlong, 36, who was friends with Ritchie-Bennett according to media reports, was also killed. "He was beautiful, intelligent, honest and fun," his parents said.

The third victim has not yet been identified.

The security source told Reuters that Saadallah had come across the radar of Britain's domestic security agency MI5 last year over intelligence he had aspirations to travel for extremist purposes, although his plans then came to nothing.

"The security services have records on thousands of people and rightly so," said Patel, adding she was limited in what she could say because the investigation was live.

Prime Minister Boris Johnson said he was "appalled and sickened" by the incident and said "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, the judge noted Saadallah's various mental health issues in reducing the sentence.

Saadallah was released from prison earlier this month, it is understood, and the COVID-19 pandemic played no part in the decision to free him.

The Sun reported he left the Bullingdon prison in Oxfordshire, 17 days ago after less than half of his sentence.

"What you appear to have here is a lone actor and they are obviously particularly hard to detect," said Jonathan Hall, the Independent Reviewer of Terrorism Legislation, whose job is to inform public debate on security laws.

"If, as has been reported, the individual is suffering from poor mental health that is a particularly difficult area."

Shocked residents of Reading, about 65 km west of London, held a minute's silence on Monday morning.

The attack was reminiscent of some recent incidents in Britain that authorities also called terrorism.

In February, police shot dead a man, previously jailed for promoting violent Islamist material, who had stabbed two people on a busy street in south London.

Last November, another man who had been jailed for terrorism offences stabbed two people to death on London Bridge before he too was shot dead by police.

Australian Associated Press