Here is the closest temporally I could find - Pinkerton's Modern Geography printed in London in 1807, seen here.

You can see on the plate between pages 16 & 17 that the map is labeled much as we would a modern map, except without the political boundaries. By this time, England had come to an understanding with the US that the United States did possess territorial sovereignty, though exactly where the line was drawn was debated and unclear. The British maintained forts in the Great Lakes and Ohio River region, despite the Treaty of Paris 1783, and impressed American sailors into the British Navy on the pretense that the sailors were British men in disguise (White, The Middle Ground). Despite these, British publications still recoginized that there was a new Republic occupying the coast of North America. Geographical and political works published in the 1790s recognized this. As one example, Winterbotham wrote a 4 volume set on the history and geography of the West Indian and North American colonies, including the United States. In his title, he recognizes the United States as a new entity (publishing in 1795), as the title reads An Historical....View of the American United States, and the European Settlements in America and the West Indies.

Also see Beckford's Descriptive Account of the Island of Jamaica printed in 1790. He specifically discusses trade between the West Indian colonies and the United States. And in Payne's Universal Geography published in 1793 in Dublin, you can see for the section on the United States he states "and the Independent United States, formed by the late Revolution in the Northern Division of the Continent (North America)."