The man held on suspicion of killing three people at a park in Reading was known to MI5, security sources say.
Khairi Saadallah, 25, from the town, was arrested on Saturday and police say they are not looking for anyone else over the terror incident.
Sources told the BBC he is originally from Libya and came to the attention of MI5 in 2019.
One victim has been named as teacher James Furlong – described by his family as “a wonderful man”.
Paying tribute to Mr Furlong, 36, head of history, government and politics at The Holt School in Wokingham, his parents Gary and Janet said: “He was beautiful, intelligent, honest and fun.”
PM Boris Johnson said he was “appalled and sickened” by the attack in Forbury Gardens on Saturday evening.
Counter Terrorism Policing South East (CTSPE) said a 25-year-old man from Reading, who was arrested initially on suspicion of murder on Saturday, has now been re-arrested under Section 41 of the Terrorism Act 2000.
Security sources said the suspect came to the attention of the security services after they received information he had aspirations to travel abroad – potentially for terrorism, according to the BBC’s home affairs correspondent Dominic Casciani.
When the information was further investigated, as the first stage of looking into a potential lead, no genuine threat or immediate…