In one sense, John and the Brits are analagous to King George and the colonists.
John’s abuse led to the “revolt” that produced the Magna Carta.
George’s abuse of the colonies led to the Declaration of Independence.
Johns abuse led to the revolt that produced the Magna Carta.
Georges abuse of the colonies led to the Declaration of Independence.
That's not quite the case.
John was incompetent and a complete failure. All of this was made even more glaring by the fact that he followed two strong and fairly successful kings.
The American colonies had been growing apart from the British since the first colonists came to America. The French and Indian War was extremely expensive and the British thought America should pay for some of it. These abuses eventually resulted in the Revolution; a major factor in the Revolution was George's pride, otherwise it is likely that Parliament would have withdrawn the troops much sooner.
However, the Revolution aside, George III was extremely popular with the British. His reign saw the defeat of Napoleon and solidified Britain's power for the next century. Granted he suffered from dementia, blindness and other ailments in the last decade or so of his reign (during which time his son served as Regent), but he remained popular.
It was during the reign of George III that the British monarchy allowed Parliament to assume ever more control of politics and saw the emergence of a true constitutional monarchy.
The general opinion of Britons today is that George III was incredibly successful. American independence was inevitable at some point and aside from the period surrounding the War of 1812 America has always enjoyed great relations with the UK.