Prime Minister Theresa May has told MPs: “We will never waver in the face of terrorism.”
Paying 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.”
Delivering a Commons statement she said Wednesday’s attacker was British born and known to police and MI5. The attack was related to “Islamist ideology”.
Labour leader Jeremy Corbyn described the attack as “an appalling atrocity”.
Four people died, including the attacker, with 40 more injured.
Mrs May said the victims included 12 Britons, three French children, two people from Romania, four from South Korea, one from Germany, one from Poland, one from Ireland, one from China, one from Italy, one from the US and two Greek people.
She 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 said it was still believed that the attacker acted alone and there was “no reason to believe” further attacks on the public were planned.
“His identity is known to the police and MI5 and when operational considerations allow, he will be publicly identified,” she said.
“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.”
Describing it as an attack on free people all over the world, Mrs May 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,” she 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.”
Mrs May also paid tribute to Foreign Office minister Tobias Ellwood, who tried to save the life of PC Palmer by giving him mouth-to-mouth resuscitation and attempting to stem the flow of blood from his stab wounds in New Palace Yard.
And she praised the police for “heroically” doing their job by stopping the attacker getting access to Parliamentary buildings by shooting him dead “within 20 yards of the gate”.
“If his intention was to gain access to this building, we should be clear that he did not succeed,” she said.
She also said it was wrong to describe the attack as Islamic, claiming it was “Islamist terrorism – it’s a perversion of a great faith”.
Mr Corbyn said MPs were “united by our humanity, by our democratic values and by that human impulse for solidarity to stand together in times of darkness and adversity”.
“I express my condolences to the family and friends of PC Keith Palmer, who gave his life yesterday in defence of the public and our democracy – and to the loved ones of those still in a critical condition, including the French schoolchildren visiting our capital from Concarneau in Brittany,” he said.
“The injured include people of ten nationalities. Innocent people were killed yesterday walking across Westminster Bridge as many millions of Londoners and tourists have done before them.”
Conservative MP James Cleverly fought back tears as he paid tribute to his friend PC Palmer, who he met 25 years ago in the Royal Artillery. He asked Mrs May whether the police officer’s “gallantry and sacrifice” could be recognised posthumously – to which she replied, that this would be considered in due course.
SNP Westminster leader Angus Robertson said: “Today of all days we are reminded, notwithstanding our differences on political and constitutional issues, we are as one in our dedication to democracy, rule of law and harmony between people of all faiths and none.”
He wished Mrs May and Home Secretary Amber Rudd well in their work in the aftermath of the “appalling, indiscriminate, terrorist act”.
Liberal Democrat leader Tim Farron said MPs were “beyond thankful to the police, to the NHS, to the emergency services, actually to the staff of this House, in keeping us safe and being so utterly dedicated to their roles”.
He said: “Those who attack us hate our freedom, our peaceful democracy, our love of country, our tolerance, our openness and our unity.”
Nigel Dodds, deputy leader of the Democratic Unionist Party, said PC Palmer “and his colleagues are the reason that we’re here today and every other day”.
Over in the House of Lords, the Archbishop of Canterbury said: “Yesterday afternoon, one of our own security staff at Lambeth Palace – a Muslim – arrived at the gate having been missed by the vehicle very narrowly, and spent time helping those who’d been injured.
“It was typical of this community in this country that he refused to go home until the end of his shift, and simply spent the time doing his job as he expected.”
But outside Parliament, UKIP leader Paul Nuttall called on the Muslim community to help cut out the “cancer within our society of radical Islam”.
He said security needed to be heightened, adding that “all that was needed for this terrorist attack to take place yesterday was a Hyundai 4×4 and a couple of kitchen knives”.
Earlier MPs, peers, police and workers around Whitehall observed a one minute’s silence.
Commons deputy speaker Lindsay Hoyle said Parliament’s security committee will hold an emergency meeting later on Thursday to discuss security arrangements on the estate.
Speaking beside a police cordon outside Parliament, Mr Hoyle told BBC Breakfast: “We’re in a village and our village policeman has been murdered and all of our thoughts are with the family and the other innocent victims.
“But of course the House must continue – we will not give in to terrorism and today we’ll continue.
Mr Hoyle, who is also chairman of the security committee, said: “We will be having an emergency meeting. We’ll be getting information – what else needs to be put in place – and we will reflect.”
He said there would be support for MPs and staff who “witnessed things they never expected to witness in their lives”, he said.
Mrs May has spoken to Mr Trump, German Chancellor Angela Merkel, French President Francois Hollande and Romanian President Klaus Iohannis in the period since the attack, and will speak to more foreign leaders over the course of Thursday, Downing Street said.
The PM’s official spokesman said Mrs May had been “focused entirely on this issue since it happened” and was in constant contact with police and security services.
He declined to discuss whether any changes had been made to her schedule for the coming days.