Answering this gets us into some tricky counterfactual arguments: i.e. "what would have happened if______ ?".

Negotiations pre-1775 for some sort of peaceable arrangement failed, and were not resumed: communications across the Atlantic were quite slow, and the appointed representatives of the British government of Lord North and King George III were military men, Generals Gage, Howe and Clinton. Their objective ( and the King's and Lord North's) was also military- to crush the rebellion of the colonists. They tried to do that in Massachusetts, but it spread to New York and beyond, gaining more popular support and getting French assistance. General Clinton then attempted to shift the conflict to the southern colonies, where there were more Loyalists: the assumption was that, with the southern colonies secured, they would become a base of operations from with the rebellion in the north could be contained and finally eliminated. That strategy did not work, either: the British had already lost the support of quite a few in the southern elite with Virginia governor Dunmore's Proclamation offering freedom to Blacks who escaped Patriot masters. But also the army found that though it could ask the help of Loyalists, it could not actually defend them from the violent reprisals of Patriot groups. The south was never secured. Nor were the British successful in bringing the main Continental forces to a big pitched battle and defeating them: after his defeat in the Battle of Long Island, George Washington would avoid such things, mostly reserving his forces for good opportunities, like at Trenton, and finally at Yorktown.

There was a continuously changing situation, 1775-1782, in which there was growing popular support for the revolt within the colonies, growing foreign assistance ( especially from France) and more and more voices within the British government questioning whether simply trying to crush the revolt was a good idea.

So, we can only speculate : what would have happened if the revolt had stayed in Massachusetts? Or if non-military men arrived to deal with the situation, in 1775? What would have happened if Lord North and King George had not been so insistent on war, had listened to people like MP Issac Barré? What would have happened if the French hadn't helped, or if Washington had tried fighting pitched battles even after his disaster at Long Island? Maybe most importantly, what would have happened if Britain had sent enough soldiers to actually occupy all of the enormous colonial territory, instead of only enough to defeat a colonial army- if they could catch it?

Also importantly, the North American colonies were among the least important of Britain's concerns- they were far less valuable than the Caribbean ones, and there was no sign the revolt would spread to there, or to Canada. Britain had other conflicts, as well: it was just starting to get more involved in India, where an initial commercial enterprise would grow to be a colonial war. And the American revolt had brought it into war, once again, with France and Spain. A British victory at the time might well have looked like what they got: abandoning an annoying quagmire of a war, abandoning a colonial backwater to its fate, and getting on with more profitable enterprises.