The international terror threat level to the UK has been reduced from severe to substantial, Home Secretary Theresa May has said.
But a terrorist attack remains a strong possibility and might well occur without further warning, she said.
Mrs May said: "The change in the threat level to substantial does not mean the overall threat has gone away - there remains a real and serious threat against the United Kingdom and I would ask the public to remain vigilant."
Mrs May went on: "Today the Joint Terrorism Analysis Centre (JTAC) changed the UK threat level from international terrorism from severe to substantial.
"This means that a terrorist attack is a strong possibility and might well occur without further warning.
"The decision to change the threat level is taken by JTAC independently of ministers and is based on the very latest intelligence, considering factors such as capability, intent and timescale.
"Substantial continues to indicate a high level of threat and the threat level is kept under constant review."
There are five levels of threat, ranging from low, meaning an attack is unlikely, to critical, when an attack is expected imminently.
The threat level was first made public on August 1, 2006, when it was set at severe. It was raised to critical on August 10 that year after a series of arrests over an alleged plot to blow up transatlantic aircraft, but lowered to severe again the following week.
The threat level was last at critical in June 2007, following the attack on Glasgow Airport and the failed car bombings in central London.