Why did the British want to capture cities of Washington in New Orleans?

The British were not interested in capturing the cities of Washington nor New Orleans.

During the War of 1812, the United States fought against the British. The cities of Washington, D.C., and New Orleans were both American cities. The British did attack and burn down the White House in Washington, D.C., but they were not trying to capture the city itself. In New Orleans, the British landed troops and attacked the city, but they were defeated by the Americans.