Who controlled the Charlestown Peninsula in 1775?

At that time the British were in control of the Charlestown Peninsula. In that year the famous Battle of Bunker Hill took place on the peninsula, which ended in a Pyrrhic victory for the British—that is, a victory which left them worse off than before. British losses were far greater than those of the American colonists. Although the Americans technically lost the battle, they nonetheless achieved a spectacular moral victory, one that provided a huge boost for the colonists' morale.
However, the Battle of Bunker Hill caused immense damage and destruction, with the town of Breed's Hill, where most of the fighting took place, being almost completely destroyed. Although the British remained in control of the Charlestown Peninsula, their political and military authority had been fatally undermined by the heavy losses they'd sustained at Bunker Hill.