Representatives from the two boxing squads were present at the launch of the second year of the British Lionhearts in the Community (BLITC) programme here, which finished just as the horrific incident was unfolding at around 2:40pm local time.
One of the victims of the attack was killed when a car drove at high speed on Westminster Bridge and into pedestrians, leaving dozens of others with serious injuries.
The car then crashed before the assailant continued the attack on foot and tried to gain access to the Palace of Westminster, fatally stabbing a police officer before he was shot dead.
The policeman has since been named as 48-year-old Keith Palmer.
Foreign Office Minister Tobias Ellwood was seen giving mouth-to-mouth resuscitation to the officer.
A woman was also reportedly pulled alive from the River Thames, although she had severe injuries.
There are not yet any other confirmed casualties.
Three of those injured on Westminster Bridge were from a group of French schoolchildren, while four students Edge Hill University in Lancashire were also hurt, with two being described as "walking wounded".
Two police officers are said to be in a serious condition.
Acting Deputy Commissioner and head of counter terrorism at the Metropolitan Police Mark Rowley told reporters at New Scotland Yard that a major investigation was underway into a "marauding terrorist attack".
British Lionhearts super heavyweight boxer Frazer Clarke appears to have been one of the closest of the athletes to the incident.
He Tweeted: "I can never unsee what I've just seen in front of my eyes at the House of Parliament [sic] in London.
"God be with the police officer.
"Currently inside the lobby at the Houses of Parliament terrible scenes.
"God be with that police officer!! Get me out of here ASAP."
The Italia Thunder also issued a statement on Twitter in their native language, reassuring their fans and followers that they were okay.
"Not a good start [to] the adventure in London," the post read.
"Although at the time of the incident some of the #ItaliaThunder boxers were not far away, we want to reassure you that all are well."
Coe, a member of the House of Lords, and IAAF communications director Jackie Brock-Doyle were also visiting Westminster at the time of the incident.
They were among several hundred people forced to wait in buildings around Westminster, spending several hours there before being evacuated.
Witnesses heard gunshots just outside of the building before the entire area was placed under lockdown by police and security officers.
Members of Parliament (MPs), who were in attendance at the House of Commons to vote on a pension bill, which came after Theresa May held her Prime Minister's Questions, were kept inside for over four hours along with hundreds of others, including journalists, staff and tour groups.
Around 1,000 people were then evacuated to nearby Westminster Abbey, where they were processed.
In the evening, May chaired an emergency meeting of the Cobra Committee, the British Government's emergency council for major security issues.
The British Prime Minister described the attack as "sick and depraved" in an address outside Downing Street this evening.
"For those of us who were in Parliament at the time of this attack, these events provide a particular reminder of the exceptional bravery of our police and security services who risk their lives to keep us safe," she said.
"Once again today, these exceptional men and women ran towards the danger, even as they encouraged others to move the other way.
"On behalf of the whole country I want to pay tribute to them and to all our emergency services for the work they have been doing to reassure the public.
"The location of this attack was no accident.
"The terrorist chose to strike at the heart of our capital city, where people of all nationalities, religions and cultures come together to celebrate the values of liberty, democracy and freedom of speech."