How important were the 13 colonies to the British Empire?

The 13 Colonies were a very important part of the British Empire. In the end, however, they were not indispensable.
In 1700, only about 250,000 people lived in the 13 Colonies. By 1760, the population had grown to 2.2 million, and Philadelphia was the second largest city—behind London—in the British Empire.
In commerce and industry, too, the 13 Colonies were increasing in importance. The Americans were often more innovative than their British counterparts, and they increasingly resented British control over their economic affairs.
Britain tried to levy new taxes on the Colonies after the end of the French and Indian War in 1763. The war with the French had been expensive, and London expected the colonists to contribute to the costs. The Americans were angry because they did not have direct representation in the British House of Commons.
The dispute over taxation was a key factor which led to the Revolutionary War (1775–1783). The war dragged on and became too expensive for the British. Also, after France took the Americans's side, Britain decided that it could not win. Britain sought peace and consolidated the rest of its still-considerable empire. Indeed, in 1800, the British Empire included Canada, small parts of the Americas, India, Australia, and New Zealand. Losing the 13 Colonies was a serious—but not mortal—blow to Britain.