On the whole I agree with the others who are saying that it wasn’t taught much British history classes, and even at the time it was seen as a pretty minor issue compared to other stuff that Britain had going on at the time. Indeed, I suspect that if Britain had been bothered to deploy the full might of their military power against the American rebels, they could have been crushed quite easily. (No doubt many Americans will be quick tell me I am totally wrong about that.)
Apart from history classes, however, Britain gets so much American entertainment (movies, TV, even books), that I suspect that most British people who learn about the American revolution largely from this, tend to see it largely from the American perspective. They might tend to block out any “British are evil” aspects of the storytelling, but they will still take on board the view of the revolutionaries as the good guys, fighting for freedom and all that.
Having come from Britain to live in America, however, I have been struck by the fact that Americans always refer to it as the Revolution, whereas in Britain I always heard it referred to as the American War of Independence (never even anything like “rebellion,” which sounds like a revolution, but is less positive). The phrase “American War of Independence,” when I think about it, does not make much sense. From the British perspective I can see why one might say “War of American Independence” (i.e., the war we fought over the issue of American independence), but “American War of Independence” seems to mean a war the Americans fought over independence (which it was, of course, but if you are going to be looking at from the American perspective like this, why not just say "revolution like the Americans themselves do).
Incidentally, on one of my first Fourth of Julys in America I was asked by an American friend, a very intelligent and well educated man, whether we celebrate the Fourth in Britain. I replied, “No, we do not consider the loss of the American colonies to be cause for celebration.” (I am rather proud of that.)
Also, if the movie “The Madness of King George” is to be believed, George III did not actually go mad until long after the colonies had been lost.