Military personnel will now be deployed to protect key sites under the new threat level.
The 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.
BBC security correspondent Frank Gardner 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".