Speaking after chairing a meeting of the Government’s emergency COBRA committee, the Prime Minister condemned the “cowardly” terror attack at Parsons Green station during Friday morning’s rush hour.
Mrs May said the UK’s terror threat level will stay at severe, meaning an attack is highly likely, although this is going to be kept under review.
She also confirmed that there will be an increased armed police presence on the capital’s transport network, and urged the public to “go about their daily lives but remain vigilant”.
The PM added: “The police and the security services are obviously doing all the work to discover the full circumstances of this cowardly attack.
“The threat of terrorism that we face is severe, but by working together we will defeat them.”
At least 22 people were injured in the blast aboard the District line train in west London, including children.
While most victims suffered flash burns, some were hurt in the ensuing panic as people fled.
Counter-terror police, who are being assisted by MI5, are scouring CCTV in their hunt for the bomber.
Investigators are also examining the improvised explosive device, which is understood to have had a timer.
Photographs from the scene showed a large flaming bucket with wires coming from it on the floor of the carriage.
The blast comes as the UK remains on high alert following a series of terror attacks in Manchester, Westminster, London Bridge and Finsbury Park this year.
Mrs May added: “We do need to ensure we are dealing with not just the terrorist threat but with the extremism and the hate that can actually incite that terrorism.
“That is why we are looking very carefully at the powers that our police and security services have to make sure they have the powers they need.”
The PM also slapped down US President Donald Trump over his tweet in which he claimed the Parsons Green bomber had been “in the sights” of Scotland Yard and stressed the need to be “proactive”.
Mrs May said: “I never think it’s helpful for anybody to speculate on what is an ongoing investigation.”
The Metropolitan Police also said Mr Trump’s comments were “unhelpful” and “pure speculation”.
London Mayor Sadiq Khan, who clashed with Mr Trump over his response to the London Bridge terror attack, would not be drawn on the president’s comments
Simply been too busy this morning to look at my Twitter,” he told LBC Radio.
“My priority is making sure that we do what we can do to keep London safe.”
A City Hall source said: “He hopes people don’t speculate on things before we know the full facts. That’s quite clear what he thinks about that.”