The second arrest came the same day police detained an 18-year-old man "on suspicion of being concerned in the commission, preparation or instigation of acts of terrorism" in connection with the bombing.
The UK terror threat level has been lowered to severe after being raised to critical, its highest level, following Friday's attack on a London train station.
A Metropolitan Police spokesman said a building in the town was being searched.
Images posted on social media following the Parsons Green attack appeared to show wires protruding from a flaming bucket inside a plastic Lidl carrier bag on the floor of a carriage.
The two arrests indicate police and security services believe the attack was part of a coordinated plot, not the act of a single person.
"We are still pursing numerous lines of enquiry and at a great pace", said Neil Basu, counter-terrorism coordinator for the London police.
He was taken to a south London police station and remains in custody.
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.
One of the homes is in Sunbury, less than an hour west of central London, where a couple served as foster parents for many children, including refugees, over several decades.
The couple, who have taken in 268 children over four decades, including at least eight refugees, are staying with friends as their home continues to be scoured by counter-terrorism investigators.
Local residents said the man living at the property in Lowlands Drive, Stanwell, which was raided by police on Sunday, is a light-skinned man of Arabic appearance.
The improvised device, which failed to fully detonate, was packed with fairy lights and is thought to have contained triacetone triperoxide (TATP) explosives, the same powerful explosive used in the 7/7 attacks in London and other deadly bombings across Europe. Officials say 30 people were injured, including some hurt in the panic that ensued, and all but one have been released from the hospital. "That was shut down, it didn't happen again", she said, adding that the relationship with the USA security services was very important to the UK.
Britain had been warned that a terrorist attack could be "imminent" after the bomb suspect fled the scene and went on the run.
Earlier this year, assailants with vans and knives attacked passers by on Westminster Bridge and London Bridge in two separate strikes, and a van was driven into worshippers outside a mosque in Finsbury Park.
Ben Wallace said: "I totally agree that CCTV footage is extremely useful and I have no doubt at some stage that will come but the conduct of the investigation I leave to the police and security services, and why and what they do with that information".