Five people have died and at least 40 were injured after an attacker drove a car along a pavement in Westminster, stabbed a policeman and was shot dead by police in the grounds of Parliament.
The dead officer has been named as PC Keith Palmer, 48, a husband and father.
PM Theresa May said the attack on Wednesday was "sick and depraved" and struck at values of liberty, democracy and freedom of speech.
The attacker has not been named by police.
Acting Deputy Commissioner and head of counter terrorism at the Metropolitan Police, Mark Rowley, said they think they know who he is and that he was inspired by international and Islamist-related terrorism, but gave no further details.
The attack unfolded at about 14.40 GMT on Wednesday when a single attacker drove a grey Hyundai i40 along a pavement over Westminster Bridge, near the Houses of Parliament in central London, killing three people and injuring many more.
The car then crashed into railings outside the Houses of Parliament.
The attacker, armed with a knife, ran to Parliament where he was confronted by the police. PC Palmer - who was not armed - was then stabbed and killed.
The attacker was shot dead by armed officers.
Mr Rowley paid tribute to PC Palmer, saying: "He was someone who left for work today expecting to return home at the end of his shift, and he had every right to expect that would happen."
"Heartbroken" former colleague, Conservative MP James Cleverly, paid tribute to the "lovely man" he had known for 25 years. The pair had served together in the Royal Artillery before PC Palmer became a policeman.
Foreign Office minister Tobias Ellwood - a former Army officer whose brother died in the Bali terrorist bombing in 2002 - attempted mouth-to-mouth resuscitation of Pc Palmer.
The attacker's other victims have not been named yet. One is known to be a woman.