The UK’s threat level has been lowered from critical to severe after two people were arrested in connection with the terror attack on Parsons Green.
Home Secretary Amber Rudd said police had made good progress in the investigation as she announced the country had been removed from the highest terror alert.
An 18-year-old man and a 21-year-old man remain in custody after being arrested by police on Saturday and searches are under way at two addresses.
Details have emerged about the youngest suspect, who a local politician claimed was an Iraqi refugee who moved to the country aged 15 when his parents died.
Assistant Commissioner Mark Rowley, the country’s top counter-terrorism officer, said developments in the operation had provided greater clarity on the attack.
He said: “We are getting a greater understanding of the preparation of the device.
“There is still much more to do but this greater clarity and this progress has led JTAC - the independent body that assesses threat - to come to the judgement that an attack is no longer imminent.”
An address in Stanwell, Surrey - just metres from the runway at Heathrow Terminal 5 - is being searched in connection with the arrest of the 21-year-old man in Hounslow late on Saturday evening, Scotland Yard said.
An 18-year-old man was earlier detained in the departure area of Dover ferry port, which is the busiest ferry hub in Europe and a gateway to the French coast.
Police are continuing to search a second house in Sunbury-on-Thames, Surrey - home to Penelope and Ronald Jones, aged 71 and 88 respectively, who previously received MBEs for services to children and families.
A family friend, who asked not to be named, said the 18-year-old suspect had recently left the care of the couple, who have been foster parents for almost 40 years and taken in up to 300 children, including eight refugees.
She told the Press Association: “He has only been there a few weeks, he was a refugee. He moved out a few weeks ago - he turned 18 and left.
“I’m pretty sure that he had come from Surrey social services.”
She said she had known Mr and Mrs Jones for around eight years and had a family connection to them.
“I was shocked when I heard. It is horrible when you know them,” she said.
“They are kind people. Penny is such a nice person - she would give you the shirt off her back.”
A local politician said he understood the 18-year-old suspect to be an Iraqi orphan who had moved to Britain aged 15 after his parents died.
Leader of Spelthorne Borough Council Ian Harvey, whose ward is Sunbury East, said he learnt about the boy’s background from neighbours of Mr and Mrs Jones and information available publicly.
He said: “One thing I understand is that he was an Iraqi refugee who came here aged 15 - his parents died in Iraq.”
Jim Adaway, a family friend, said Mr and Mrs Jones recently returned to foster caring to help resettle youngsters from overseas.
The 37-year-old said Mrs Jones had been struggling with one of the children in their care.
He said: “I think Penny was getting in touch with (the authorities) saying ‘I cannot handle this one’.”
The couple are said to be staying with friends following the police raids, during which surrounding houses were evacuated by counter-terror officers, with residents told they had “one minute” to flee their homes.
The man who lives in the Stanwell address raided by police on Sunday is a light-skinned man of Arabic appearance, according to local residents.
He is described as having dark, frizzy hair and is around 5ft 7ins or 5ft 8ins tall.
According to a couple, who asked not to be named, he habitually stayed up late at night and was often visited by two male companions, who appeared to be in their late teens.
The husband said: “He seemed a really, really nice chap, we have sat there and had a drink with him, but he didn’t drink alcohol.
“He was from North Africa, I think, perhaps Morocco or Algeria, but he had family from Scotland.
“I think he moved in about 14 months ago, he was very quiet, he was on his own.
“He had two guys there that used to be there all the time with him, he would have them there through the night and they were always playing games.
“But they never had the TV on and there wasn’t a lot of furniture, his friends were about 18 or 19.”
His wife added: “We thought he was a security guard or a prison officer because of his uniform.
“To me he just kept himself to himself, he wasn’t involved with us or the neighbours, but he seemed to be up at unusual hours.
“He had pale skin and fluffy hair that was short, he didn’t own the house, we don’t know whether he was renting it off someone else.”
Thirty people were injured when the improvised device exploded during rush hour at Parsons Green station, with all but one now discharged from hospital.
The lowering of the threat level from critical to severe means another attack is no longer imminent, but still highly likely.
Mayor of London Sadiq Khan said: “I would urge all Londoners to remain vigilant over the days ahead.
“You will see more police - including armed officers - on the streets and transport network throughout the week. They are there to keep us safe.
“London’s response to this attack shows once again that we will never be intimidated by terrorism.”
Armed police will maintain a strong presence across the country, while military personnel drafted in to provide support will be phased out.