Final answer:
Britain wanted to take New Orleans by surprise to gain control over the Mississippi River, which was strategically important for trade and transportation.
Step-by-step explanation:
The cause for Britain wanting to take New Orleans by surprise was to gain control over the Mississippi River. The strategic position of New Orleans near the mouth of the river made it an important location for trade and transportation, especially with the rise of steam-powered river traffic in the nineteenth century. By controlling New Orleans, Britain would have had a significant advantage in terms of trade and military presence in North America.