I'm not convinced, but as far as I'm aware, the last battle Britain fought against America was against the Yankees in the War of Independence and not against the USA as such. Since then, there have been no battles fought between the two nations, unless you include economic and cultural scuffles as well.
The Battle of Greenham Common!!
seriously I think it was the battle of New Orleans (1814)
not part of the wars of independence but as a result of America invading Canada.