Police said in they arrested a 21-year-old man in the west London suburb of Hounslow, which is home to London's Heathrow Airport, just before midnight Saturday.
He was arrested by the Kent Police under the Terrorism Act and remains in custody at a London police station.
Following the bombing of a London tube train at Parsons Green station on Friday, the terror threat level was increased from severe to critical.
Police are continuing to search a house in Sunbury-on-Thames in Surrey.
Earlier an 18-year-old teenager was arrested in the departure area of the port of Dover in connection with the attack on Saturday morning.
Residents of the neighborhood say the house that was searched is occupied by an elderly couple - Penelope and Ronald Jones - who have taken care of foster children for decades.
In the wake of the bombing, police hinted they were searching for more than one suspect, and said they were keeping an "open mind" as to whether multiple people were involved.
She added there was "no evidence" to back up Islamic State's claim there were more "live" explosive devices.
Rudd made the comments on BBC's Andrew Marr Show on Sunday, after Trump claimed the person who carried out the attack was known to British police.
"It's never helpful to have speculation about an ongoing operation and I would include the President of the United States in that comment, " said Rudd.
Amber Rudd praised the police for the progress they have made in the investigation and called on the public to remain vigilant after Prime Minister Theresa May put Britain on the highest security level of "critical".
The blast was the fifth major terrorist attack in Britain this year.
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