What was the conflict between Great Britain and the colonies over sovereignty?

For the sake of the question, I am going to assume that you mean the American colonies. Between 1660 and approximately 1763, the British Parliament practiced salutary neglect in its relationship toward the colonies. While Parliament passed taxation laws and laws governing colonial trade, it made no real effort to enforce these laws. This left the colonies to govern themselves as they pleased. It was not uncommon for the colonies to trade with France and Spain even though these nations were enemies of Britain. Tax collectors were either bought off or generally ignored.
All of this changed after the French and Indian War. Thanks to this war, British officials received a close look at how the colonies seemed to disregard Parliament. Parliament stated that the colonists must pay their fair share toward the defense of the empire. The colonists felt as though their contribution toward the French and Indian War was discounted, and they resented the extra oversight. When the colonists stated that they were not represented in Parliament, Parliament said that it was not a representative body and that any Member of Parliament was qualified to speak for the entire realm. This would ultimately lead to the split between the colonists and Britain in the Revolutionary War.