The attack was claimed by the Islamic State terror group.
"The bombing on a metro in London was carried out by a detachment of the Islamic State," it said in a statement published by its Amaq propaganda agency.
The explosion, on a District Line Tube in the British capital's southwest, occurred as the train pulled into Parsons Green station. Commuters said they heard a bang and saw a fireball inside the carriage when the "bucket bomb" exploded.
Pictures of a white bucket on fire inside a supermarket bag, with wires trailing on to the carriage floor of the train went viral on social media.
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Investigators were examining what appears to be a circuit board recovered from the scene, news reports said.
Scotland Yard said it was a terror incident and they "assess" an IED triggered the blast. A hunt was on for a suspect the British media labelled as the "bucket bomber".
Some reports indicated that the suspect was identified after investigators reviewed the CCTV footage at the station.
The London Ambulance Service said 29 people have been treated in hospital. Police said that 'most' had 'flash burns'.
Assistant Commissioner Mark Rowley said more police would be deployed in London, particularly on the transport network, but refused to say whether anyone had been arrested.
Prime Minister May said the incident was a "cowardly" act "clearly intended to cause significant harm".
Addressing the media after chairing an emergency response COBRA committee meeting at Downing Street, May said the UK's terror threat level remains unchanged for now, at "severe" - the second highest.
"We do need to ensure that we are dealing with, not just the terrorist threat but with the extremism and the hate that can actually incite that terrorism." the prime minister added.
The police later in an updated statement said an area of 50 metres in radius around the station has been evacuated as a precaution in case the bomb left on the train remains unstable.
Mayor Sadiq Khan said London "utterly condemns the hideous individuals who attempt to use terror to harm us and destroy our way of life", and urged Londoners to remain calm and vigilant.
"Deputy Assistant Commissioner Neil Basu, the senior national coordinator for counter-terrorism policing, has declared it a terrorist incident," the police said in a statement earlier in the day.
"The Metropolitan Police Service and British Transport Police attended the scene, along with colleagues from the London Fire Brigade and London Ambulance Service. At present we are aware of a number of people who have suffered injuries," it said, adding that the station remains cordoned off and "we are advising people to avoid the area."
Downing Street said May was "receiving regular updates".
Eyewitnesses outside the station reported seeing people with facial injuries. Many have been told to stay in lockdown as police evacuated the area and placed a wide zone under a police cordon.
Passenger Chris Wildish told the BBC that he saw a bucket in a supermarket bag with "low-level flames coming out of it" by the door of the rear carriage.
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