The move came after investigators were unable to rule out whether Manchester bombing suspect Salman Abedi acted alone, the prime minister said, BBC news wrote.
Military personnel will now be deployed to protect key sites.
Twenty-two people were killed and 59 injured when a suicide bomber attacked Manchester Arena on Monday evening.
Read alsoUPDATE: Manchester Arena blast kills 22, injures 59 - BBCThe prime minister said soldiers would be placed in key public locations to support armed police in protecting the public.
Military personnel may also be seen at other events over the coming weeks, such as concerts, Mrs May said, working under the command of police officers.
Read also"Ukraine stands together with Britain": Poroshenko condemns Manchester terrorist attackBBC says the number of UK troops deployed will be in the hundreds not around the 5,000 figure being reported.
The prime minister said she did not want the public to feel "unduly alarmed" but said it was a "proportionate and sensible response".
