This is the fourth time that the assessment has been placed at the highest level in the past 11 years.
Mrs May also said military personnel will replace police officers on guard duties, and warned the public would see a greater presence of armed police on the streets.
And she also urged the public to go about their “business in a normal way.”
Theresa May said: “The joint terrorism and analysis centre, the independent organisation responsible for setting the threat level on the basis of available intelligence has now decided to raise it from severe to critical.
“This means that a further attack may be imminent. Following JTAC decision, the police have asked for authorisation from the Secretary of Defence to enact part of the first phase of Operation Tempera.
“This is well established plan to derive military support to the police.
“Military personnel are going to replace police officers on guard duty at certain protected sights that are accessible to the public.
“The public will see more armed police officers on the transport network and on our streets providing extra protection and this is a proportionate and sensible step which will provide extra reassurances and protection while the investigation progresses.”
The Met Police later gave a press conference, in which they added military back up has ensured “1,000 armed police officers have been freed up across the country to provide extra reassurance” to the public.
Officers will be placed in transport hubs, at events and in crowded places , some in uniform and some operating covertly.
A spoeksman added the public should “remain vigilant as you go about your weekend and if you do see anything that concerns you, please act on your instincts and don’t hesitate to call us.
The explosion devastated the District line train, bound for central London, which had just stopped at Parsons Green station in west London at just gone 8am.
Emergency services including police, fire and ambulance raced to the scene after the improvised explosive device detonated in a carriage.
Witnesses said they saw a white “builder’s bucket” in a supermarket bag, and pictures online appeared to show wires protruding from it on the floor of a carriage. Reports suggested the device had a timer.
The Islamic State terror group has claimed responsibility for the Parsons Green attack.
The Amaq News agency said a “detachment” from the terror group was responsible for this morning’s blast, according to US-base Site Intelligence.
The claim is…