There is an interesting Wiki article that sums up the degree to which martial events in the New World were influenced by those in the Old - This One. The Nine Years' War, to begin with, the wars of the Spanish and Austrian Succession, and the better-known Seven Years' War that pitted Frederick the Great against Maria Theresa and a very young George Washington against the French several thousand miles away in what we term the French and Indian War. The American War of Independence, in which the French got their revenge against the British for the latter's takeover in Quebec. The French Revolution, in which the French paid for the debt they'd incurred tweaking the British nose in America. The Napoleonic Wars, in which the British stopped an astonishing French expansion, and to which the War of 1812 served as an interlude between the Grand Armee's disaster in Russia, and the Hundred Days and Waterloo.
Napoleon got his own future revenge in the New World in 1803 by selling Jefferson's administration the Louisiana Purchase, openly proclaiming he did so as a geostrategic move against the British, and as it eventually turned out, a stunningly successful one. And so, in my opinion, the British might be forgiven for viewing with considerable apprehension in 1812, the present and inevitable U.S. expansion to both the west and the north. To the north they managed to hold a line. To the west, it was hopeless.
There, however, it took some time to work itself out. The slogan "54-40 or fight" represented American expansionism not simply into British territory but abutting Russian claims. By 1846, when that was working itself out, Texas had already won independence and was setting up for the Mexican-American War, wherein the issue was claims the new Mexican government had inherited from both the Spanish and the French.
It is only outside this context that one can adhere to the strange and rather provincial claims of historians such as Howard Zinn that America must be judged in isolation and as inherently aggressive, imperialistic, oppressive, and evil. Despite the separation of the Atlantic ocean events in the New World were very much a function of events in the Old. In a sense events in the Old such as the French Revolution were a function of a reverse influence. If the honest reader does not attempt to understand it all together he doesn't stand much of a chance of understanding it at all. Just my $0.02.
You make a good point about Britain's apprehension over our westward expansion. Secretly, when the time was right, the British planned to argue that Napoleon lacked the authority to sell the Louisiana to the U.S., on the theory that France had usurped the throne of Spain thereby making the treaty that ceded the Spanish claim to the Louisiana Territory to France a nullity. Not knowing this, the American negotiators in Ghent were puzzled over what they saw as some apparently harmless but overly technical language in the treaty that the British government insisted on, but which could have been used later to justify Britain's refusal to return any territory in Louisiana that they might have occupied by conquest. It was Andrew Jackson that put "paid" to that plan.
Britain tried again later when it offered to take the Republic of Texas under its wing, making it a British territory. Britain's thought at the time, not unjustified, was that this would be an acceptable compromise to both Mexico and the Texans, and once again put a brake on our expansion westward. They came close to success: as the debate over slavery made the prospect of admitting Texas as a state seem more and more unlikely, many in Texas saw an alliance with Britain as their only practical option.