The Prime Minister addressed MPs as they gathered at the usual time inside the Palace of Westminster, which a day before had come under attack from a knife-wielding terrorist.
An hour after MPs had stood for a minute’s silence in honour of the innocent people killed in the attack, Mrs May delivered a statement with details of the atrocity.
She said it was still believed that the attacker acted alone and there was “no reason to believe” further attacks on the public were planned.
She added: “His identity is known to the police and MI5 and when operational considerations allow, he will be publicly identified.
“What I can confirm is that the man was British-born and that some years ago he was once investigated by MI5 in relation to concerns about violent extremism.
“He was a peripheral figure. The case is historic. He was not part of the current intelligence picture.
“There was no prior intelligence of his intent or of the plot.”
APaying tribute to Pc Keith Palmer, who died after being stabbed, she said: “He was every inch a hero and his actions will never be forgotten.”
Mrs May told MPs: “Yesterday an act of terrorism tried to silence our democracy, but today we meet as normal, as generations have done before us and as future generations will continue to do, to deliver a simple message: ‘We are not afraid and our resolve will never waver in the face of terrorism’.”
She told the House of Commons that Parliament was sending out the message following Wednesday’s attack: “We will never waver in the face of terrorism.”
Mrs May said it was an attack on free people all over the world as she thanked global allies including US President Donald Trump for their support.
“We meet here in the oldest of all parliaments because we know that democracy and the values it entails will always prevail,” the PM said.
“Those values - free speech, liberty, human rights, and the rule of law - are embodied here in this place but they are shared by free people around the world.
“A terrorist came to the place where people of all nationalities and cultures gather to celebrate what it means to be free.
“And he took out his rage indiscriminately against innocent men, women and children.
“This was an attack on free people everywhere, and on behalf of the British people I would like to thank our friends and allies around the world who have made it clear that they stand with us at this time.”