Kenya stepped up security after sending troops into neighbouring Somalia last October to pursue Islamist al Shabaab rebels, whom it blames for a string of kidnappings and cross-border attacks, often targeting tourists.
"We believe that terrorists may be in the final stages of planning attacks. Attacks could be indiscriminate and target Kenyan institutions as well as places where expatriates and foreign travellers gather," the Foreign Office statement said.
London did not change its overall advice - to avoid non-essential travel within 60 km of the border with Somalia or in coastal areas within 150 km of the border.
Britain has close ties with Kenya, which it ruled as a colony until independence in 1963. London's Metropolitan Police sent a counter terrorism team to Kenya last month to assist with investigations into a Briton suspected of planning an attack.
Nairobi police chief Anthony Kibuchi was quoted by a local paper on Friday as saying there had been new threats of attacks in the capital by al Qaeda, with which al Shabaab is allied.
But when contacted by Reuters after Britain's warning, he said there was no new, specific threat against Nairobi.
"The statement I gave is 'normal alerts'," he told Reuters.
"We just want to be very alert because our Kenya Defence Forces are doing a very good job in Somalia. Now the sympathisers of al Shabaab are like a wounded buffalo, very dangerous. I was just asking members of the public to be extra alert."
Deputy Police Spokesman Charles Owino said the force had been on heightened alert ever since the war on al Shabaab started, because of the potential for reprisal attacks.
Security forces said they had foiled attacks in Kenya over the holidays, through pre-emptive strikes inside Somalia and the killing of three heavily armed militants who were trying to land at Kiunga, near the border, from skiffs on New Year's Eve.
Since Kenyan forces moved into Somalia, at least 30 people, including several policemen, have been killed in attacks by suspected militants in the northeastern Kenyan districts of Wajir, Mandera and Garissa.
Another person was killed in a grenade attack in Nairobi.
"NOT FAR FROM END"
Despite the warnings of attacks, the military painted an upbeat picture of its war against the Somali militants.
"We are not very far from seeing the end of al Shabaab," Colonel Cyrus Oguna told a news conference on Saturday.
He said more than 60 al Shabaab fighters had died on Friday when Kenyan jets bombed their camp in Garbahare in southern Somalia, and that defections were mounting.
He said divisions over dwindling financial resources and how to deploy foreign fighters had split al Shabaab in two factions, led respectively by Mukhtar Robow Abu Mansour and Hassan Dahir Aweys, and by Mukhtar Abu Zubeir.
"We are going to capitalise on this by hitting them from the air, ground and sea, again and again, until their spine is broken," Oguna said.
But al Shabaab spokesman Abdiasis Abu Musab denied that al Shabaab was crumbling. "We swear we shall eliminate Kenyan troops and dig their graves in Somalia," he told Reuters.
Together with soldiers from the Somali Transitional Federal Government, the Kenyan troops are taking on al Shabaab in three sectors of southern Somalia.
They have taken several towns in the northern sector including Fafadun and El-Ade this week, but encountered stiff resistance in the central sector, where al Shabaab has dug in to prevent them advancing to the port of Kismayu, a port that is an important source of revenue for the rebels.
(Additional reporting by Jacob Kuehn and Feisal Omar in Mogadishu; Editing by Kevin Liffey)
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