William Congreve did not invent rockets or even their use in battle, but he did set up a a research program within the British Royal Arsenal in 1801 to study them. Congreve's rockets were first used in battle fired from boats during an attack on Boulogne in 1806, and afterwards at times throughout the Napoleonic wars, both from ships or boats or on land. (The fictional HMS Polychrest of Patrick O'Brian's novel "Post Captain" is inspired by the Dart-class sloops and there's a strong implication it was designed as some sort of a rocket ship.)

Congreve's experiments were inspired by rockets used by the Tipu Sultan of Mysore against British troops in India. But the first use of military rockets was in medieval China, which is way out of my league in terms of expertise.

If you're interested in further reading, Robert Wilkinson-Latham's "British Artillery on Land and Sea, 1790-1820" is a good and inexpensive resource.