The man held by police on suspicion of killing three people in Reading is Khairi Saadallah.
The 25-year-old from Reading was arrested at the scene and police say they are not looking for anyone else over the “terrorist incident”.
Security sources told the BBC he is originally from Libya.
Prime Minister Boris Johnson said he was “appalled and sickened” by the attack in a park on Saturday evening.
Mr Johnson said he had spoken to the chief constable of Thames Valley Police and praised the bravery of the unarmed officers who arrested the suspect.
A witness told the BBC that he saw a man moving between groups of people in Forbury Gardens, a park in Reading town centre, trying to stab them.
Three other people were injured in the attack.
Thames Valley Police’s chief constable, John Campbell, told reporters that a man was arrested within five minutes of the first emergency call made to police – at 18:56 BST on Saturday.
He said lives had been “devastated” by the incident, but added that there was not believed to be a wider risk to the public and there was nothing to suggest anyone else was involved in the attack.
Metropolitan Police Assistant Commissioner Neil Basu, head of counter-terrorism policing, described it as an “atrocity”.
The UK’s terrorism threat level was downgraded from “severe” to “substantial” – meaning an attack is likely – in November 2019.
Substantial is the third of five ratings at which the threat level can stand.
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