Hi,
As some others wrote, it is a last version of the "India pattern" musket first adopted by the British army in 1795. Your gun, sometimes known as the "pattern 1809" or "pattern 1810" was produced between 1809-1815 when the style was phased out and replaced by the "new land" musket. About 2 million were produced and it was the primary musket carried by British troops during the later stages of the Napoleonic war and our war of 1812. According to DeWitt Bailey and Eric Goldstein, during the brief period of peace with France in 1802, British ordnance tried to rearm its army with the pattern 1804 "new land" musket. However, war began again too quickly for that to happen and ordnance rushed to convert production to its existing India pattern musket. That arm was upgraded in 1809 and became the gun you own. After it was phased out many were sold to other countries like Mexico. However, Mexican arms usually have a Mexican surcharge stamped or engraved on the lock, which yours does not appear to have. A musket is simply a large bore military arm with a long barrel. Before the 1850s they were almost always smooth bored to make them easy and fast to load. With the advent of bullets and systems (Tighe breeches, expanding bullets, etc) allowing fast loading of rifled arms, most muskets were eventually rifled.
dave