Prime Minister Theresa May has raised the threat level to the highest possible rating, meaning another atrocity is expected imminently.
She said a "wider group of individuals" could have been involved in the Manchester Arena blast rather than just suicide bomber Abedi.
In a sign of the increased threat, the military could be deployed to support armed police officers, Mrs May added during a live televised statement from Downing Street.
Monday night's attack at a concert by US pop star Ariana Grande left 22 people dead, including an eight-year-old girl, and dozens injured.
Calling in the Army
Armed troops could be deployed on the streets to guard concert venues and sports stadiums under a plan authorised by the Government in the wake of the Manchester Arena atrocity.
Soldiers will replace armed police at many sites under Operation Temperer, which is being enacted after security experts warned the Government that another terrorist attack could be imminent.
The decision taken at a meeting of the Government's emergency Cobra committee will mean soldiers could play a key role in protecting civilians and free up armed police officers to help fight the terror threat.
Operation Temperer, which was first revealed in 2015, is believed to allow up to 5,000 troops to be deployed in support of the police.
The country's senior counter-terrorism officer said acknowledged that the use of troops was "unusual" but it would allow police to "stretch our armed capability".
Met Police Assistant Commissioner Mark Rowley said the first phase would allow soldiers to replace police officers at fixed locations but after that they could "augment our patrols" at sites such as transport hubs and major events.
"There are many big events across the country over the next couple of weeks, we are going to be working really closely with the organisers to review the security, review their stewarding arrangements, review our policing arrangements and make sure that decisions are taken that events only go ahead when it's sensible and safe to do so," he said.
The plan means soldiers could be deployed to support police at major events such as the FA Cup final at Wembley on Saturday or the Champions League final in Cardiff on June 3.
Prime Minister Theresa May said the operation had been authorised by Defence Secretary Sir Michael Fallon at the request of the police after experts at the Joint Terrorism Analysis Centre (JTAC) raised the threat level from "severe" to the highest "critical" setting.
"This request is part of a well-established plan, known as Operation Temperer, in which both the armed forces and the police officers involved are well-trained and well-prepared to work in this kind of environment," she said.
"The Secretary of State for Defence has approved this request, and Operation Temperer is now in force.
"This means that armed police officers responsible for duties such as guarding key sites will be replaced by members of the armed forces, which will allow the police to significantly increase the number of armed officers on patrol in key locations.
"You might also see military personnel deployed at certain events, such as concerts and sports matches, helping the police to keep the public safe. In all circumstances, members of the armed forces who are deployed in this way will be under the command of police officers."