On the other hand, American merchants couldn't (legally) trade with anyone but Great Britain, there could be no banks or machine manufacturers in the colonies...
The Americans paid no taxes because they already did their duty to the Empire in submitting to mercantilism. As long as smuggling was allowed to go on with the (far closer) West Indies, they really didn't care. The problem came when that smuggling was stamped upon and taxes attempted to be imposed.
Oh, I'm not saying the British were right, and the American's wrong, nor the opposite. They were both right in their way, which is why their positions were perhaps quite intractable. Perhaps the colonies were doing their bit, but at the same time they did have it easier in a great many ways than people back on the home islands. It's very difficult to balance those two viewpoints, especially when both have merit.
On Mercantalism, it's not as if it was only the American colonists were forbade trading with other nations. That was the norm for everyone, even people in the home islands. Again it's an intractable position, the colonists
are doing their bit for the mother country, but they're also asking for special treatment, from the British perspective. The reason is simple, trade in Mercantalism is seen as a Zero-Sum game, contrast that with Capitalism which sees trade as positive-sum. Under Capitalism both parties to a trade can make a profit from it, because they have different expectations and requirements going in. Mercantalist theory says that for one side to make a profit, the other has to make a loss, so by trading with other nations, you're opening yourself up to make a loss. The whole point of European colonialism by the time the French, Dutch and British were really getting involved, was to gain raw materials to make manufactured goods, without losing out on trade to other nations. Once those goods are manufactured, you sell to your countrymen first, and then any excess should be sought to be sold to foriegn nations, for precious metals.
Mercantalism was the major cause of the American War of Independence. It was also the major cause of most of the wars Britain engaged in, right up to and including the Opium Wars with China.
Personally I think the obvious best case compromise for both sides, would be to simply give the 13 Colonies representation in Parliament, at first it would only need to be (and would probably only be) a token gesture anyway. You'd then likely see a gradual expansion of voting rights in Parliament, in step with the growing representation and power of the House of Commons. Maybe you'd even seen a Federated States of the Empire of Great Britain eventually emerge? Of course then other colonies would be demanding representation in home government, and I'm saying that from a 21st Century perspective with over two centuries of hindsight. Would things be as clear then? Nope.
Talking about some amorphous 'British' opinion is missing the fact that the UK was still riven with divisions in this day. While some East Anglian MPs might be found who directly identify with people who are probably somewhat close kin in Massachusetts, a Northumberland based MP might be more willing to argue in favor of coercion against the rebels.
We really need an idea of what's meant by 'Britain's Eyes'.
I took it too mean the general, or majority stance, of the British establishment/government. If the majority stance had been to identify with the colonists, there probably wouldn't have been a war.