Given that the British didn’t have anything like the kind of resources necessary to occupy all of the American colonies, their only hope of success was some sort of dramatic victory that would destroy the morale of the Patriots. It could have happened in New York.
Washington, who had foolishly attempted to defend the city, was trapped in Brooklyn, with the Royal Navy between his army and Manhattan. Due to the incredible fortitude of his boatmen, the inattention of the Howe brothers, and very thick fog, the Continental Army managed to evacuate to safety. From the British perspective, the greatest opportunity of the war was lost. It was just as important as Saratoga and Yorktown.
But what if the evacuation had failed? Would the British have won the war? Based on our experiences in Vietnam and Afghanistan, and the fact that the war continued for several years after the British left Philadelphia with minimal activity on the part of the Continental Army, I would say no. The Patriots still controlled state and local governments all over the colonies, and had the resources to fight. They would have done so, and in the end, the British would have given up.