The British Embassy in the Turkish capital Ankara was closed on Friday for unexplained "security reasons," the Foreign Office said, while Turkish media reported that four people were detained in connection with the threat.
Germany this week closed its embassy and consular officers in Turkey over security concerns, according to Bild newspaper. The closures coincide with a shorter working week due to an Islamic holiday.
Anadolu, Turkey's state-run news agency, reported that four people were detained in connection with the threat to the two diplomatic missions, but said there was no link found to terrorist groups.
"The British Embassy Ankara will be closed to the public on Friday 16 September for security reasons," the statement from the British Foreign Office said.
The British warning also repeated its advice to avoid travel to areas close to the border with Syria and the restive south-east of the country.
"Security force operations against the PKK and related groups are ongoing in Diyarbakir. The FCO advise against all travel to the city of Diyarbakir," the statement said, referring to the Kurdistan Workers' Party.
Diyarbakir is the main city in the largely Kurdish south-east of Turkey.
Turkey has been hit by numerous terrorist attacks this year, including in Ankara and Istanbul. In July, the country suffered a bloody coup attempt.
The British ambassador in Ankara, Richard Moore, posted on his Twitter account: "Sorry long-standing UK policy not to comment on intelligence matters but working closely & cooperatively with Turkish authorities."
There has been no official Turkish comment.