Home Secretary Amber Rudd said the second arrest was an indication that "good progress" was being made int the investigation of Friday's attack that injured 30 people, all but one of whom have now been released from hospitals.
The UK terror threat level remains "critical", meaning an attack is expected "imminently".
British police say they detained a 21-year-old man in the city's south end Saturday night on suspicion of a terror offense.
She announced £24m of funding for counter-terrorism operations across the country.
Police confirmed Sunday that they were searching two houses, one in Stanwell, a village in the county of Surrey, and another in Hounslow, in West London.
Earlier Saturday, an 18-year-old man was arrested in the port area of Dover, a major ferry terminal for travel between Britain and France.
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The entire neighborhood around their house was evacuated as a precaution when the search began Saturday.
The first search, linked to the first subject, started in Sunbury Saturday afternoon at a house that belongs to an elderly couple who have for years taken in foster children, including refugees from conflict zones in Syria and Iraq.
Basu said a "number of items" were recovered from the Dover terminal, without giving further details.
"We're open-minded. If there are other people responsible it's our job to find them and that is part of the reason why we are remaining at "critical" at the moment".
Neil Basu, Senior National Co-ordinator for Counter Terrorism Policing said that "We have made a significant arrest in our investigation this morning". "Our priorities. are to identify and locate any other suspects", he added.
The Islamic State group claimed responsibility for the attack, which it said was carried out by an affiliated unit.
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"It is inevitable that so-called Islamic State, or Daesh, will reach in and try to claim responsibility", Rudd told BBC Sunday.
President Donald Trump has also riled a bit of tension as authorities in the United Kingdom continue their investigation. She cautioned that it is still an ongoing investigation.
The explosion at Parsons Green station in south-west London sparked a "wall of fire" that left passengers with burns and caused a stampede of panicking people in which some were trampled.
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 vehicle door.
"People who are traveling in London will see an increased armed police presence on the transport network and security will be increased".
London's police commissioner has called on the public to be vigilant while Britain remains on high alert after a blast on a subway in the capital.
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