Britain and the US government have previously warned of possible attacks in neighbouring Sweden, which raised its terrorism alert to the second highest level on Thursday.
"Terrorists are likely to try to carry out attacks in Denmark. Attacks could be indiscriminate, including in places frequented by foreigners," the British foreign ministry warned in an updated travel advice. The authorities in Denmark have successfully disrupted a number of planned attacks and made a number of arrests, it added.
Sweden has also said it thwarted attacks after Koran burnings and other acts against Islam's holiest text.