Police said the evacuation of the Sunbury address was a "precautionary measure", with all residents in the buildings immediately surrounding the address evacuated while the search was ongoing.
Deputy Assistant Commissioner Neil Basu, Senior National Co-ordinator for Counter Terrorism Policing, said it was a "significant arrest" but warned the public to remain cautious as investigations continue.
"Although we are pleased with the progress made, this investigation continues and the threat level remains at critical.
"The public should remain vigilant as our staff, officers and partners continue to work through this complex investigation. We are not, at this time, changing our protective security measures and the steps taken to free up extra armed officers remain in place.
The explosion happened in a London Tube carriage at Parsons Green station, west London. Photo: Supplied
"This arrest will lead to more activity from our officers. For strong investigative reasons we will not give any more details on the man we arrested at this stage."
Hundreds of police worked overnight on a major manhunt, sifting forensic clues from the recovered malfunctioning bomb, from witnesses, CCTV footage and from electronic ticket barrier records.
An injured woman is assisted by a police officer close to Parsons Green station in west London after Friday's explosion on a packed London Underground train. Photo: PA
Following the first arrest, detectives from the Met's Counter Terrorism Command are continuing to urge anyone with information about the terrorist attack to contact police.
Police had suggested there may be more than one person behind the attack, which sent a "wall of flame" through a packed train carriage.
Police and community support officers gather round a police vehicle near where the incident happened. Photo: AP
Police were reportedly working on the theory that the bomb detonated by accident and may have been intended to explode in the Westminster Tube station under Parliament House, instead of Parsons Green in south-west London.
The head of counter-terrorism policing said "our priority is to identify, locate and arrest those responsible".
The bombing incident on the train is being investigated as a terrorist attack, British authorities said. Photo: AP
A thousand military police were deployed as extra guards at nuclear power stations and other vulnerable public infrastructure and transport hubs. Armed police were patrolling London streets.
On Friday night Britain's terror threat level was raised to its highest 'critical' level, meaning an attack may be imminent. It was at that level in the days immediately following the Manchester Arena bombing, when it was believed the bomb-maker was still at large.
Friday's improvised bomb was left on a packed morning commuter train It partially detonated at 8.20am. It was the fifth terror attack this year in Britain.
Experts examining photographs of the bomb posted on social media said it showed several signs of having been assembled using a 'terrorist handbook' from the internet – for example the use of Christmas lights as detonator wiring.
The device appears to have included a timer, meaning the attacker may not have been on the train when it went off. However London's Telegraph reported the bomber was thought to have still been on the train and escaped it after their device went off prematurely.
The bomb was on a train line that connects to central London, and one branch of the line goes under Westminster. The Telegraph said anti-terror police were "working on the theory" that the intended target may have been the Tube station at Westminster.
Assistant Police Commissioner Mark Rowley said "there is no doubt in my mind that those responsible intended to cause great harm and injury".
He declined to reveal details of the bomb, but The Times reported it included nails to cause shrapnel damage. The Telegraph said it was "likely packed with ball bearings, screws or nails" to maximise damage and casualties, though the eventual explosion was not forceful enough to send them flying.
At least 29 people were injured during the attack, including a 10-year-old boy. The injuries were mostly flash burns from the bomb, which was inside a plastic builder's bucket held in a Lidl shopping bag. None of the injuries were serious or life threatening.
Some more injuries came in the panic that followed the explosion, as hundreds of commuters fled the train onto the small platform at the Parsons Green station, and down the single narrow exit staircase.
One witness said she had clung to the railing in an attempt not to trample on two layers of people who had fallen underneath her. Another saw a schoolboy crack his head on the stairs as he tumbled down.
On Friday before the arrests US President Donald Trump tweeted that the terrorists behind the attack were "in the sights of Scotland Yard". However neither security services nor police were reportedly aware of the attacker's identity.
Scotland Yard said his comments were unhelpful and "pure speculation", and Prime Minister Theresa May said "I never think it's helpful for anybody to speculate on what is an ongoing investigation".
Mr Trump's comment is likely to again inject distrust into the intelligence relationship between Britain and the US. After the Manchester bombing, police briefly took the unprecedented step of suspending the sharing of intelligence with the FBI after leaks to US media.
There has been no fatal bombing on the London Underground since the 7/7 attacks, however there have been several foiled or failed attempts.