attacks" in the Kenyan capital and that attacks "may be in the final stages of planning."
Kenyan police spokesman Eric Kiraithe admitted that despite a boost in security the threat remained, urging shopping malls to remain vigilant and to "do more" to prevent attacks.
"We don't believe that Al-Shebab activities are totally neutralised," Kiraithe told reporters on Saturday, but added that police had thwarted several recent attacks.
"We are denying those with wicked plans to operate freely," Kiraithe said.
Nairobi sent troops into Somalia to battle Shebab rebels in October after several attacks, including the kidnapping of a French woman and a British tourist -- and the killing of her husband -- damaged its key tourism industry.
The Shebab, who deny involvement in the coastal attacks, in turn vowed to attack Kenya.
"The Kenyan authorities have alerted the public to a heightened threat from terrorist attacks in Nairobi. We believe that terrorists may be in the final stages of planning attacks," Britain's statement said.
The Foreign Office did not identify any group but said attacks could be "indiscriminate" and target "Kenyan institutions as well as places where expatriates and foreign travellers gather, such as hotels, shopping centres and beaches".
"We strongly advise British nationals to exercise extra vigilance and caution in public places and at public events," the statement added.
Several people have been killed in northeast regions bordering Somalia since troops launched a cross-border campaign against the Shebab, including grenades thrown into bars and a church, and several homemade explosive devices and landmines set off.
However, Nairobi has been calm since a double hand grenade attack on a bar and a bus stop in October, a crime which a Kenyan national admitted to and was jailed for life.
Kenyan police last month also issued an arrest warrant for a believed British national, Natalie Faye Webb, for alleged links to terrorist groups.
Police have issued another arrest warrant for Habib Saleh Ghani -- also known as Abu Usama Al-Pakistani -- who is believed to hold both a Kenyan and British passport, and is suspected of links to terrorism.