The important British victory from the list you provided is Charleston. The British captured Charleston, South Carolina, in May 1780 during the American Revolutionary War, marking one of their significant successes.
However, it's worth noting that Saratoga (1777) was a crucial turning point for the Americans, leading to French support, and Yorktown (1781) was the final decisive victory for the Americans that effectively ended the war. Sullivan's Island (1776) was also a significant American victory.
If you are looking strictly for a British victory, then Charleston is the correct answer.