Foreign Office minister David Lidington, told the BBC that the risk of terrorism in the region has been ongoing for some time but that the Foreign Office would not issue its current advice to leave if there were not serious reason to do so.
The terrorism risk has been there for some time, before Mali and before the Algeria crisis of last week.
I cannot comment further on operational matters but the safety of Britons is our primary concern at the Foreign Office.
We only issue the kind of advice we have, to leave Benghazi, if we have information on a credible and imminent threat.
The Prime Minister's spokesman has reiterated the "specific threat" to Westeners in Benghazi., but would not say what that was, or whether linked to Mali and Algeria.
The Foreign Office spokesman said: "We cannot comment further on the nature of the threat at this time."
Benghazi was the stronghold of the Western-backed revolt that eventually ended Gaddafi's hold on power in Libya.
However, Britain has not had any diplomatic presence in the city since an attack on the US mission last September that killed American ambassador Chris Stevens and three of his colleagues.
The Foreign Office has been advising against travel to most of Libya since last September, but has now stepped up its warning.
We are now aware of a specific and imminent threat to westerners in Benghazi, and urge any British nationals who remain there against our advice to leave immediately.
We have updated our travel advice to reflect this. The British Embassy in Tripoli has been in contact with British nationals for whom we have contact details to alert them to the advice.
The Foreign Office today urged British nationals to leave Benghazi in Libya "in response to a specific threat to westerners".