Theresa May has said the man suspected of carrying out yesterday's attack was born in Britain - and known to anti-terror authorities.
Ms May said the man had previously been investigated by MI5 over violent extremism. However the case was historic and he was not part of the "current intelligence picture."
The Prime Minster said there was also "no prior intelligence of his intent, or of the plot" but the investigation is continuing.
Ms May praised the reaction of the public as they continue to go about their daily lives, not letting the fear of terrorism take over.
She said: "The greatest response lies in the everyday actions of ordinary people.
"We are not afraid and our resolve will never waiver in the face of terrorism. Yesterday we saw the worst of humanity but we will remember the best.
"We will remember the exceptional bravery of our police, security and emergency services."
Ms May also spoke about the police officer who was killed in the incident, saying "PC Palmer had devoted his life to the service of his country" and "was every inch a hero."
The Prime Minister ended her statement with the rallying call "let this be the message from this house and nation today: our values will prevail."