This is one of those I'm just not certain of. Yes, GB was a global power, but as Spiderman says, with great power comes great responsibility. To gather and fight a war so far away, against a very different United States than either 1776 or 1812, might permit to many competitors to grab too many other 'jewels' from the crown.
Let's consider some of the other things on England's plate in and around the 1840's time frame, in particular: 1) the Irish Potato Famine, although this isn't military, it has the potential of becoming so if too little attention is paid to it; 2) The first of a series of wars in Afghanistan (1839-1842); 3) The First Opium War (1839 - 1842); 4) Anglo-Sikh Wars (1845 - 1849); and the Burma War (1848-1849).
Also consider, England probably knows that the US is not the same nation it faced twice before, you now have a better cadre of professional officers and professional soldiers.
If there were a war, England knows it will be stretched, so it knows it's best course will be to negotiate.
I believe if there had been a war, it would have largely been a Naval one, which GB would win, and a land war, which the US would win. Eventually, both sides would seek peace, and each would seek a concession in area it won in, GB would want a concession that would serve its Navy, and the US territorial concessions.
In the end, it is my belief that the US would probably have more of Western Canada than in OTL, probably offset by lands in the Southwest that would be guaranteed to Mexico (GB would want a regional power to check the US). England would probably want trade concessions in the orient, and would probably take over Hawaii.