Islamic State says a "detachment" of the terror group was behind the attack at Parsons Green station at the height of Friday morning's rush hour.
Metropolitan Police Assistant Commissioner Mark Rowley has said police are "chasing down suspects" - but warned it is routine for IS to say they carried out attacks irrespective of whether they were involved or not.
This is the fourth time that the terror threat level has been placed at "critical" in the past 11 years - with Mr Rowley adding that the extra military support will free up 1,000 armed police officers.
Announcing the change in threat level, the Prime Minister said: "The public will see more armed police on the transport network and on our streets, providing extra protection.
"This is a proportionate and sensible step which will provide extra reassurance and protection while the investigation progresses."
Military personnel will also replace officers "on guard duties at certain protected sites which are not accessible to the public".
The Mayor of London, Sadiq Khan, said: "The national threat level has now been raised to 'critical' after the evil and cowardly terrorist attack at Parsons Green.
"As the Prime Minister has said, this is our highest level of security preparedness.
"I utterly condemn the hideous individuals who target innocent people and attempt to use terror to harm us and destroy our way of life."
Earlier, Mrs May condemned the "cowardly attack", and said the improvised explosive device was "intended to cause significant harm".
She chaired a meeting of the Government's emergency COBRA committee on Friday afternoon, and urged the public "to go about their daily lives but remain vigilant".
The Prime Minister 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."
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.
Mrs May has said the Government is "looking very carefully at the powers that our police and security services have to make sure they have the powers they need".
She has also criticised US President Donald Trump over a tweet in which he claimed the Parsons Green bomber was "in the sights" of Scotland Yard - and called such speculation was not helpful.
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."
More about: #ParsonsGreen #London #terror #LondonTube
