Two people have been arrested as part of the probe into the attack, which injured passengers on a train at Parsons Green.
British police are questioning an 18-year-old man arrested in the departure lounge of the port of Dover on Saturday and another suspect, 21, detained hours later in the west London suburb of Hounslow.
He was charged under section 41 of the UK's Terrorism Act.
British police are still holding two suspects in custody over the London subway blast as commuters head to work Monday in the first morning rush hour since the attack.
With the terror threat level dropping to "severe", it signifies an attack is no longer imminent but still considered highly likely. None of the injuries was life-threatening, and experts said it appears the main charge of the bomb didn't detonate.
Britain's interior minister said a claim by U.S. President Donald Trump that the culprits behind a bombing on a London train were in the sights of the police, made on Twitter shortly after the attack, had been nothing more than speculation.
The second arrest took place in Hounslow, London- a few miles away from Heathrow Airport- on Saturday night at 11.50pm.
Queen Elizabeth II awarded the couple for their services to children in 2010.
Critics said Trump seized upon an attempt by Khan to calm the public about a stepped-up police deployment, using an out-of-context quote to imply that the mayor had said the attack - rather than the visible armed police presence in its aftermath - was no cause for alarm.
Police have searched several properties, including a home in Sunbury where an elderly couple served as foster parents for many children over several decades.
The Islamic State group claimed responsibility for the explosion.
"Photos posted on social media show a white plastic bucket with flames coming out of the top - along with wires", NPR's Frank Langfitt reported for our Newscast Unit.
Four other violent attacks in Britain this year have killed 36 people. The other attacks, near Parliament, on London Bridge and near a mosque in Finsbury Park in north London, involved vehicles and, in two cases, knives.