At least 29 people were injured in the blast
The terror threat level in Britain has been raised from severe to critical - the highest level possible.
This means an attack is expected imminently.
It comes after the Islamic State group claimed responsibility for an attack on a London Underground train on Friday morning.
It said a "detachment" of the terror group was behind the attack at Parsons Green station.
British Prime Minister Theresa May has condemned the "cowardly" terror attack on a packed London Underground train as she vowed to defeat the extremists.
Speaking after chairing a meeting of the UK government's COBRA emergency committee earlier, Mrs May said there would be an increased armed police presence on London's transport network.
She said: "The police and the security services are obviously doing all the work to discover the full circumstances of this cowardly attack."
At least 29 people, including children, were injured in the blast on the District Line in west London.
While most victims suffered flash burns, some were hurt in the ensuing panic as people fled.
Terror police, who are being assisted by intelligence agency MI5, have identified the suspected bomber.
Investigators are examining the improvised explosive device, which is understood to have had a timer.
Images show a large flaming bucket with wires coming from it on the floor of the carriage.
The Met’s Counter Terrorism Command are investigating after the incident at #ParsonsGreen tube station is declared a terrorist incident— Metropolitan Police (@metpoliceuk) September 15, 2017
The incident happened at around 8.20am.
Met Police Assistant Commissioner Mark Rowley said: "There are many urgent inquiries ongoing with hundreds of detectives involved, looking at CCTV, carrying out forensic work and speaking to witnesses."
Mayor of London, Sadiq Khan, has condemned the attack, saying the city will "never be intimidated or defeated by terrorism".
Foreign Affairs Minister Simon Coveney said he was shocked by the news from London.
He said: "My department is monitoring the situation closely through the Irish embassy in London and the consular division in Dublin. As of now, we have no indications to suggest that any Irish citizens have been affected."
Taoiseach says the Irish Embassy in London reports that no citizens are reported to be caught up in today's events.— Chris Donoghue (@chrisrdonoghue) September 15, 2017
Anyone with concerns for Irish citizens in London can contact 00-353-(1)-4082-527.
"On behalf of the Irish Government, I wish to express our solidarity with the people of London at this time", Minister Coveney added.
US President Donald Trump responded to the incident on Twitter, condemning a 'loser terrorist'.
He suggested: "Loser terrorists must be dealt with in a much tougher manner. The internet is their main recruitment tool which we must cut off & use better!"
Another attack in London by a loser terrorist.These are sick and demented people who were in the sights of Scotland Yard. Must be proactive!— Donald J. Trump (@realDonaldTrump) September 15, 2017
Media technology consultant Richard Aylmer-Hall said: "There were a few crush injuries on the stairs.
"People got squashed and crushed going down the stairs. Police evacuated everyone from the scene pretty quickly.
He added: "It was total chaotic panic. A lady who had been on the same carriage as the device described it going off - a puff of smoke and flames coming out of it."
A photo shared on social media showed a smouldering white container in a bag.
The incident has led to the closure of a number of London Underground stations, with the District Line partially suspended.
Natasha Wills, of the London Ambulance Service, said: "We were called at 8.20am to reports of an incident at Parsons Green underground station.
"We have sent multiple resources to the scene including single responders in cars, ambulance crews, incident response officers and our hazardous area response team, with the first of our medics arriving in under five minutes.
"Our initial priority is to assess the level and nature of injuries. More information will follow when we have it."