Anne Keothavong gave the British team a flying start as she took her record for the week to 3-0 with a 4-6 6-4 6-2 win over Hanne-Skak Jensen.
But Katie O'Brien lost a third straight singles rubber as she went down 2-6 6-1 2-6 to Caroline Wozniacki.
With the tie poised at 1-1 Elena Baltacha and Keothavong teamed up against Wozniacki and Eva Dyrberg in the doubles rubber, but were beaten 3-6 2-6 as Denmark ensured they will stay in Europe/Africa Zone I for 2009.
