The attacker, identified as 35-year-old Jihad Al-Shamie, a British citizen of Syrian descent, was shot dead by police following the incident.
Three individuals – two men and one woman – have been arrested on suspicion of planning a terror attack in connection with the killings.
Al-Shamie, who was not known to police or security services, rammed people with a car and stabbed a man, though worshippers and security staff prevented him from entering the synagogue.
Prime Minister Sir Keir Starmer pledged increased police protection for Jewish communities across the UK while Greater Manchester mayor Andy Burnham condemned the "horrific antisemitic attack".