Ms Mordaunt was yards away from the knifeman, in New Palace Yard, when he stabbed a police officer and attempted to charge into the Houses of Parliament yesterday afternoon.
Officers screamed at the her and other bystanders to flee as armed guards opened fire on the terrorist.
The shaken MP darted across the yard and into a nearby tube station to escape.
Reports last night when The News went to print confirmed five people were killed in the attack.
The attacker drove into people on Westminster Bridge before bursting through the gates into the front yard of the parliamentary compound.
One of the people who died was 48-year-old unarmed officer Keith Palmer, who was stabbed, while two others were pedestrians on the bridge. Another member of the public was also killed.
The attacker was shot and killed by police.
Reliving the horrifying ordeal Ms Mordaunt, the former armed forces minister, told The News: ‘I could hear the gunshots and the police telling us to run.
‘I got out via an entrance that goes to the underground.
‘I was just running and trying to evacuate people to get them out.’
Police said at least 40 people were injured including three officers.
The deadly assault began on Westminster Bridge, where the suspect mowed down a number of pedestrians before crashing his car into railings.
Clutching his knife, having stabbed PC Palmer, the attacker was reported to have been approaching a second officer when he was shot.
Ms Mordaunt added she was ‘heartbroken’ by the death of the police officer.
Much of the city centre was placed on lockdown, including the House of Commons.
Among those caught up in the ordeal were Portsmouth South MP Flick Drummond, Fareham MP Suella Fernandes, Gosport MP Caroline Dinenage and Havant MP Alan Mak.
Speaking at the time from inside the chamber, Mrs Drummond told The News: ‘It is confusing. We don’t know what has happened exactly.
‘We’re all very calm in here. We’re not allowed to leave until the Speaker of the House says we can.
‘The Prime Minister has been bundled away somewhere, which is good.’
The MPs and members of the public were allowed out of the Commons at about 7pm.
They gathered at Westminster Abbey afterwards.
Ms Fernandes said: ‘It’s frightening and I get upset when I think about the policeman who has been stabbed.
‘The staff here have been on guard to protect members of the public and MPs here.
‘They really do put their lives on the line.’
She added: ‘You see all these atrocious attacks in the news and you never think that it will happen on your doorstep.
‘I didn’t really believe it. I thought it was a joke or some kind of mistake.’
Mr Mak paid tribute to the swift response of police and parliamentary security staff for tackling the attacker.
‘This is very reassuring,’ he said.
‘They were very professional.’
Armed police swarmed around the Palace of Westminster as Scotland Yard revealed it had launched a major counter-terrorism investigation into the attack.
Paramedics rushed to Westminster Bridge and the Houses of Parliament to treat the wounded.
An air ambulance was also called upon to treat the terror suspect – who has not been formally identified.
It was suggested by Scotland Yard’s top anti-terror officer Mark Rowley that police were aware of who the assailant was.
He told reporters: ‘This was a day we’ve planned for but hoped would never happen. Sadly it is now a reality.’
Last night, Hampshire police’s chief constable Olivia Pinkney posted on Twitter the force would be looking at security.
She said: ‘Our priority is to keep you safe and we are reviewing security in light of this incident.’
An earlier tweet said: ‘Thoughts for those involved today, and with the friends, family and colleagues of the brave officer who has died.’
Last night, a parliamentary spokesman said both the House of Commons and Lords will sit at their usual times today. The Commons will sit at 9.30am while the Lords will convene at 11am.
It is not yet known whether any special steps will be taken in the chamber.
The attack came on the first anniversary of the Brussels terror atrocity, where 32 people were killed and 320 hurt.