I'm actually reading Chernow's Washington: A Life right now, which is excellent. He cites one British officer, who said only that the Declaration "served to highlight 'the villainy and the madness of these deluded people'" (p. 237).

From other conduct referenced in Chernow's book, it's clear, though, that the British command did not take the Declaration seriously. For example, during the run-up to the New York campaign, communiques to George Washington from the British commander, General Howe, were initially addressed to "George Washington, Esq.," or "George Washington &c &c." By avoiding reference to Washington's commission as General by the Continental Congress, Howe was implying that the Congress, as it was not sovereign, had no authority to appoint anyone to anything. Thus, Howe's letters addressed Washington as a gentleman but not as the representative of a sovereign nation.

Washington returned the letters until Howe addressed him as "General."