Britain believes militants are completing plans to attack Kenyan institutions as well as places frequented by expatriates and tourists, the British Foreign Office said on Saturday.
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.
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.
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.