The British, even with heavy losses, still have control of the seas at the end of the day. Additionally, their shipyard can churn out ships at a very quick rate, much faster than the American shipyards can in 1914. So the RN is certain to win. And they'd likely keep up a blockade once they gained dominance of the seas.
On land, it would likely end in favor of the Americans, and Canada would be overrun. However, this might be averted with the help of the BEF and other colonial forces (like from Australia or India). Furthermore, even if Canada is overrun, that won't change the economic situation that would be brought about by a British blockade (although there is the possibility that the US could become self-sufficient).
As for supplies, the British get their oil from the Middle East, within their spheres of influence. So they'll be fine there. This area, though, is their one true disadvantage. The US's industrial capacity is truly far greater than the UK's, and the US will easily outproduce the British over a long period of time. So any victory for Britain would need to be hard-fought and quickly won.