The thing is, in OTL, the British did 'win' the War of 1812. The US got it ass kick out of Canada, DC got burned to the ground, etc. The reason why many see it as a draw is in part of New Orleans, (After the treaty.) some American victories at sea, (Old Iron Sides) at the Great Lakes, and Fort Henry.
The British war goal was basically to put the Americans in their place, and they got that. The main objective to simply end the war and they got that. They didn't particularly want to fight the Americans at all. The British are not fools, they won the war and then gave the US nearly everything they'd asked for since it really didn't cost England much at all and would help keep the peace for years. Even if they had much more success I doubt Britain would have demanded territorial concessions. If they tried, you have another war down the line, and by then, the USA would be much stronger then years before.
At the very much, if you have to, they take Minnesota, Wisconsin, and part of Maine, but that's it, even then, it be hard without pissing off the USA.
Heck, even today the whole War of 1812 is a afterthought to the United Kingdom.