The 18-year-old's arrest took place at the Dover ferry terminal, a main link to Europe, and a "number of items" were recovered during the operation.
The couple who own the foster home 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. He was arrested under Britain's Terrorism Act.
British police and spy agencies have not found evidence that last week's attack on a London commuter train was ordered or organized by a recognized militant group, according to USA and British government sources familiar with the investigation.
British Prime Minister Theresa May raised the city's terror threat level to "critical" - meaning an attack is imminent - but downgraded it Sunday to "severe" - meaning an attack is highly likely.
British police questioned two suspects on Monday - an 18-year-old Iraqi refugee who is believed to have planted a homemade explosive device on a packed rush-hour subway carriage in west London on Friday, and a 21-year-old from Syria, who is named by police as Yahyah Farroukh.
Basu also said investigators were keeping an "open mind" as to whether more than one person was involved in the attack.
He said: "We are getting a greater understanding of the preparation of the device".
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Rudd said a key focus was to ensure that there was less material available to radicalise young people. The president tweeted hours after the attack Friday that United Kingdom police had had the perpetrators in their sights.
British Prime Minister Theresa May had already rebuked the US leader for the remark, saying, "I never think it's helpful for anybody to speculate on what is an ongoing investigation".
Images of the bomb posted on social media appear to show a bucket on fire that had been placed inside a plastic bag close to a rail auto door.
Ms Rudd also said that over the next week military personnel would be returning to their original positons as London attempts to resume normality after its fifth terror attack this year.
London police said their investigation into Friday's attack is being supported by MI-5, Britain's domestic intelligence agency.
Mayor of London Sadiq Khan said: "I would urge all Londoners to remain vigilant over the days ahead".