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Detectives said a man had run into a park in Reading, about 40 miles (65 km) west of London where locals had been enjoying the evening sun on Saturday, and attacked people with a knife before being tackled by unarmed officers five minutes after they were alerted.
Police said an unnamed 25-year-old man who had initially been detained on suspicion of murder had since been re-arrested under the Terrorism Act. He remains in police custody.
"The investigation continues to move at a fast pace," said Detective Chief Superintendent Kath Barnes, head of the regional counter-terrorism unit.
A Western security source, speaking on condition of anonymity, told Reuters that the arrested man was a Libyan called Khairi Saadallah.
The security source said 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 came to nothing.
He never met the criteria for a full investigation, the source said.
Initially police and the government had said the attack did not appear to be terrorism. But Britain's most senior counter-terrorism police officer, Neil Basu, said officers had worked through the night and had now declared it to be a terrorist incident.
"This was an atrocity," Basu said. "From our enquiries undertaken so far, officers have found nothing to suggest that there were any other people involved in the attack, and presently, we are not looking for anyone else in relation to this incident."
'APPALLED AND SICKENED'
While the motivation for the attack was unclear, he said there was no intelligence other crowded places were at risk.
The victims have not yet been formally identified but a school in a nearby town said one of its teachers, James Furlong, had been killed.
Prime Minister Boris Johnson said he was "appalled and sickened" by the attack and said Britain would change the law if needed to prevent any future incidents.
"If there are lessons we need to learn ... we will learn those lessons and we will not hesitate to take action if necessary," he said.
A witness said the attack began in Reading's Forbury Gardens when a man suddenly shouted unintelligibly and then veered towards a group of about eight to 10 friends and began stabbing them.
"He darted round anti-clockwise the circle, got one, went to another, stabbed the next one, went to another, stabbed the next one," Lawrence Wort, 20, told BBC TV. "He stood up and I saw a massive knife in his hand, probably at least 5 inches (13 cm) minimum."
The attack took place after a Black Lives Matter rally by anti-racism protesters in the park which concluded three hours earlier but Basu said the two incidents were not related.
Current coronavirus restrictions mean venues like pubs are closed, so many people in Britain gather in parks in the evenings to meet friends.
The nature of the attack was reminiscent of a number of recent incidents in Britain that authorities considered to be 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.
Britain also suffered four attacks in 2017, the most deadly of them a suicide bombing at the end of a concert by U.S. singer Ariana Grande in Manchester, northern England.