Saturday's announcement came two months after bombings against three luxury hotels in the capital Amman that killed 60 people plus three bombers and wounded about 100 more.
The embassy said in an update posted on its website: "Terrorists may be in the final stages of planning attacks against Westerners and places frequented by Westerners.
"If you are planning to travel to Jordan, you should take sensible precautions for your personal security arrangements throughout your visit," the update added, while acknowledging that "most visits are trouble-free".
"You should take extra care at the borders with Israel and Iraq," the embassy urged.
But Nasser Jawdeh, the Jordanian government spokesman, said there was no reason to close the embassy, based on investigations into the specific intelligence held by the British.
"The Jordanian security services have dealt seriously with the threat received by the embassy of Great Britain in Amman, have compared it with intelligence they have and concluded that this does not warrant closing the embassy, which has been communicated to the embassy."
"Terrorists may be in the final stages of planning attacks against Westerners and places frequented by Westerners"
UK embassy statement
He added, however, that security had been beefed up around the mission and in the neighbourhood.
The 9 November attacks were claimed by the Iraq-based al-Qaida group of Jordanian-born Islamist Abu Musab al-Zarqawi, who has threatened new attacks on his homeland.
The attacks triggered shock in Jordan, one of the most stable Arab countries and a key US ally, where the government has pledged to launch a "preventive war against terrorism".
In August, a Jordanian soldier was killed in a rocket attack in the southern port city of Aqaba, also blamed on al-Zarqawi's group.
He already faces a death sentence in Jordan over the 2002 murder of a US diplomat and is the most wanted man in Iraq, where there is a $25 million bounty for his death or capture.
Al-Zarqawi, once described as a "thug" by King Abdullah II, was released from jail in 1999 as part of a royal pardon when the monarch took office after the death of his father King Hussein.
About 51,000 Britons visited Jordan in 2004, the last year for which figures were available.