But photos of casualties lying on the ground - before they got help - and people taking selfies have caused revulsion.
Referring to the man posing for a selfie, one said: "Sir you with the selfie stick, you need that shoving up your a***."
One person said: "Unbelievable, how could someone think that it's acceptable to do that."
Parveen Agnihotri commented: "Shame on the people taking selfies rather than helping the injured. Seems like we've become a nation of uncaring self promotion."
Kavita Cooper said: "Touched by the bravery of those that ran towards victims to offer help and support. Disgusted by those taking selfies."
Another added: "Unbelievable! Some people disgusting! Please track this sick individual down & shame him publicly at the very least!"
One said: "What is wrong with some people man. No brains at all. Muppet."
It followed similar outrage caused by people posing for selfies following terror attacks elsewhere.
Scotland Yard said the attack, which comes a year to the day after terrorist atrocities in Brussels, is being treated "as a terrorist incident until we know otherwise".
At least 10 people were hit on Westminster bridge when a Hyundai 4x4 drove along the pavement, knocking down pedestrians before crashing into a fence below Big Ben.
One victim of the car attack was left floating face down in the Thames but was pulled from the river alive.
The terror suspect, an Asian man in his 40s, then broke into the grounds of Parliament and stabbed a police officer before he was shot.
In the aftermath of the attack, the hundreds of people inside Parliament were warned to stay away from any windows before being evacuated.
Armed police from the Met's elite terror squad combed the estate to ensure it was secure, keeping people in the 900-year-old Westminster Hall.
Prime Minister Theresa May was later seen being bundled into the back seat of her silver Jaguar surrounded by armed guards.
A counter-terrorism investigation is already under way, police said.