How did the battle of Bunker Hill change Britain's view of the colonist?

Throughout the war, the question was would the colonists fight? The British thought that they could have one quick decisive victory and that afterward the colonists would give up. Though the British did win the first battle, the the Battle of Bunker Hill, it was at a great cost, and they now saw that the colonists were a substantial threat that could not just be brushed aside.

They discovered they could fight, wouldnt back down, in it to win it