The terror threat level is being increased from severe to critical, indicating that a further attack is imminent, Prime Minister Theresa May said.
Mrs May added that military personnel could be deployed to support armed police officers as a sign of the increased threat.
She added that "it is a possibility" a wider group of individuals were involved in the Manchester attack, rather than just suicide bomber Salman Abedi.
In a live televised statement from Downing Street, the Prime Minister said the terror threat level would be increased to "critical", meaning an attack was expected imminently.
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.
Speaking at Number 10, Mrs May said: "The spirit of Manchester and the spirit of Britain is far mightier than the sick plots of depraved terrorists.
"That is why the terrorists will never win and we will prevail.
In my statement earlier today, I said that the police and security services needed to investigate whether Abedi was acting alone. Those investigations continue.
"But the work undertaken throughout the day has revealed it is a possibility we cannot ignore that there is a wider group of individuals linked to this attack.
"This morning I said that the Joint Terrorism Analysis Centre, the independent organisation responsible for setting the threat level on the basis of the intelligence available, was keeping the threat level under constant review.
"It has now concluded, on the basis of today's investigations, that the threat level should be increased for the time being from severe to critical."