That's a complicated question which depends on the precise boundaries of the definitions you choose.

There's the example of Egypt, which had a revolution against British rule in 1919 that was promptly followed by recognition of Egyptian independence.

There's the example of South Africa, where a series of wars led eventually to a negotiated independence several years later.

There's the example of India, where a long independence movement followed by a series of strikes and mutinies post-WWII led to granting of independence.

And there's the example of Ireland, where a 3 year long period of revolution followed by civil war led to the effective independence of Southern Ireland and then a truce followed by the Anglo-Irish treaty formally recognized that independence. However, it's important to recognize that the UK was in the process of granting successive levels of home rule to Ireland (though it's also important to understand the brutality of British occupation of Ireland and the potential significant difference between abstract home rule in the future and concrete independence.)

So there is a spectrum of events from America and Ireland over on the "won independence through revolution" side with Egypt, India, and South Africa somewhere in the "were granted independence possibly because dealing with the revolution was seen as too much of a hassle" middle and then over on the other side you have, say, Canada in the "didn't cause a ruckus and eventually was granted full sovereign independence" side.

The reasons for desiring independence are varied. In general the British Empire was a very classist system, with a very divergent system of expectations, rights, privileges, and opportunities depending on who you were, where you were born, where you lived, and your ethnicity. In India, for example, the local population was bled dry through taxation and many Indians were subjected to conditions scarcely better than serfdom or slavery even up through the early 20th century. Moreover, mutinies and protests were often suppressed with brutal violence and the massacre of thousands upon thousands of civilians. Additionally, famines causing the deaths of millions were essentially just tolerated by the British as the cost of doing business. Similarly, the Irish were constantly treated as second class citizens, routinely subjected to depredations and violence, while the British exploited them economically. You see the same sort of pattern throughout much of the British Empire, despite the high sounding ideals espoused by those in power. In practice there were millions upon millions of people with effectively no real rights and certainly no opportunity to attain equality or economic parity with white British born citizens. For example, even affluent and educated Indians who attended colleges in England were never treated as remotely equal to whites.

As for the Americans, the story is different but still similar in the outlines. Many Americans had wealth, status, and education. American colonies had local elected governments. And yet it was as though all of this was in a sandbox isolated from Britain itself. Through the 18th century as the American colonies grew and became sizable cities and economic powerhouses Americans began to see themselves as British citizens on equal footing to anyone living on the British Isles. And yet they clearly were not. Not only did they lack proper representation in the British Parliament (and so were incapable of influencing government policy) but they were denied basic legal rights that had been granted to British citizens for centuries. They were at once fully enmeshed in British society, economy, and governance and at the same time completely excluded. They eventually came to see this as untenable, and initially they sought to gain status but then quickly chose instead that independence was the only reasonable option open to them.

Some readings:

• Punjabi Century, 1857-1947 by Prakash Tandon
• Behind Mud Walls by William and Charlotte Wiser