What did the british win after they won at Battle of Bunker Hill?

After the British victory at the Battle of Bunker Hill on June 17, 1775, they gained control of the Charlestown Peninsula, which included key strategic positions overlooking Boston. However, the battle proved costly for the British, with significant casualties that bolstered American resolve and support for the Revolutionary War. While they secured the immediate area, the heavy losses highlighted the challenges they would face in suppressing the colonial rebellion. Ultimately, the battle demonstrated that the Americans could stand up to British forces, setting the stage for future confrontations.