GB was a monarchy
By 1812 Britain was a Constitutional monarchy, in which the power to declare war was vested in the Parliment. For that matter it still is. It WAS a democratic nation in 1812 in the sense that it was a democratic nation in 1914 and in 2005
The last king that believed Britain was a monarchy had the government disagree with him to the point where he lost his head over the issue.
No, by then most power was with Parliament.