A 25-year-old man from Reading was arrested at the scene of the attack at about 19:00 BST on Saturday, which also left three people seriously injured.
Metropolitan Police Assistant Commissioner Neil Basu, head of counter-terrorism policing, said: "This was an atrocity."
He said police have found "nothing to suggest anyone else was involved".
Security sources told the BBC the man arrested is thought to be Libyan.
Mr Basu said police were working with the coroner to formally identify those who had died and he praised the actions of unarmed Thames Valley Police officers, who detained the suspect.
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