The Prime Minister paid tribute to the emergency services for their work and to those who had lost their lives in the sickening attack.
She said: “Our thoughts and prayers go out to all that have been affected, to the victims themselves and their family and friends who waved their loved ones off but will not now be welcoming them home.”
Mrs May then said those threatening the values of “freedom” and “democracy” were “doomed to failure”.
She said: “Parliament, democracy, freedom, human rights, the rule of law command the admiration and respect of free people everywhere.
Theresa May speaks following the London terror attack
“That is why is a target for those who reject those values.”
She continued: “Attempts to defeat those values through violence and terror is doomed to failure.
“Tomorrow morning, Parliament will meet as normal.”
She insisted the British public would continue to remain defiant in the face of the terror threat in London.
London Terror Attack: LIVE PICTURES Wed, March 22, 2017
Two dead, 12 injured as knifeman mows into crowd in Westminster
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Conservative MP Tobias Ellwood (centre) helps emergency services attend to a police officer outside the Palace of Westminster, London
She said: “Londoners and others from around the world who have come here to visit this great city will get up and go about their days as normal.
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“We will all move forward together, never giving in to terror and never allowing the voices of hate and evil to drive us apart.”
The address comes after four people, including a police officer and the attacker, died as a result of the incident.
About 20 people are thought to have been injured.
Mrs May confirmed the knifeman attempted to storm the Houses of Parliament before he was shot dead and members of the public were mowed down on the street outside at about 2.30pm.