Police stepped up security around the embassies, which are in the same neighborhood of the capital, Jakarta.
A police officer who declined to be named said the source of the bomb threats said the embassies would be targeted at 10 p.m. Thursday or 10 a.m. Friday. Both deadlines passed without any explosion.
The British Foreign Office said services at the embassy would remain suspended while officials monitor the security situation in the Indonesian capital.
"Obviously the safety of staff and visitors is paramount," it said in a statement. "The closure will not have a detrimental effect on the relief operations in Aceh following the tsunami of 26 December."
The Foreign Office's travel Web site also warned that the threat of terrorism remains high in Indonesia.
"We continue to receive reports that terrorists in Indonesia are planning further attacks on Westerners and Western interests," it said. "Attacks could occur at any time, anywhere in Indonesia and are likely to be directed against locations frequented by foreigners.
"Terrorists have shown in previous attacks, like the attack on the Australian Embassy (search) and the Bali bombings, that they have the means and the motivation to carry out successful attacks."