Counterterrorism agencies are said to have detected "chatter" relating to a repeat of the Islamic State (IS) extremist group practice of filming and posting execution videos.
According to the newspaper, the country's security services reacted to the potential threat after viewing a tweet posted by a jihadist in Syria.
Earlier in January, UK Home Secretary Theresa May said that the country's threat level remained at "severe," which meant that an attack was "highly likely." The alert level was raised after a gun massacre at the French weekly magazine Charlie Hebdo, in which terrorists killed 12 people.
The militants said that the killings of journalists and aid workers are a response to US-led coalition airstrikes targeting IS positions in Iraq and Syria.