An 18-year-old man and a 21-year-old were arrested separately by police on Saturday and searches are under way at two addresses on the outskirts of London, according to UK police.
Both men had been fostered by the same elderly couple, and at least one was a refugee from Iraq, local officials told CNN Monday.
The 18-year-old was arrested by police in the departure lounge of Dover ferry port, which is the busiest ferry hub in Europe and a gateway to the French coast, the police said Saturday.
The second man was picked up by police at a fast food takeaway, Aladdin's, in East Hounslow, a west London suburb on the way to Heathrow Airport, at around 11:50 pm on Saturday night, police confirmed.
A local shopkeeper, who didn't want to be named, said the 21-year-old "came here shopping every once in while. He just bought milk and soft drinks, he was just a regular folk, and that's all I know".
Local council leader Ian Harvey told CNN the 18-year-old suspect was fostered by an elderly couple, Ronald and Penelope Jones, and was living with them at the time of the attack on Friday.
He said local residents had told him the teen was an Iraqi asylum seeker who had come to the United Kingdom three years ago after his parents were killed in Iraq. Harvey described the teenager as unhappy.
A local official said the second suspect had also been fostered by the Joneses. That source asked not to be named because he was not authorized to release the information.
Couple honored by Queen for fostering children
Queen Elizabeth II honored Ronald and Penelope Jones for their fostering work in 2010, awarding them MBEs (Member of the Order of the British Empire) "for services to children and families."
Alison Griffiths, another local official, described the Joneses as "the sort of people who would never turn a child away, no matter what the circumstances."
Griffiths, a Surrey County councillor, said the Joneses had fostered over 280 children in 30 years.
They have fostered around eight refugees in the past year, including children from Afghanistan and Iraq, she said.
Police were continuing Monday to search their house in Sunbury-on-Thames, Surrey, on the outskirts of west London, PA reported.
"We can confirm that a search is taking place at a residential address in Stanwell, in connection with the arrest in Hounslow," Surrey police said in a statement.
British TV showed images of the house as backing right on to the runway of Heathrow Airport.
Assistant Commissioner Mark Rowley, National Lead for Counter Terrorism Policing, announced Sunday evening the second arrest and that the police were lowering the threat the UK was under from international terrorism from critical to severe.
Shortly after the explosion on Friday, ISIS claimed involvement via its Amaq News Agency.
But when asked if ISIS may have had a hand in the attack, UK Home Secretary Amber Rudd said: "It is inevitable that so-called Islamic State or Daesh will reach in and try and claim responsibility. We have no evidence to suggest that yet."
Rudd said the government is releasing an additional £24 million ($32.6 million) for counter-terrorism operations around the country, "particularly to support operations where they are protecting people in public places."