I know Britain probably wouldn't support the south this much, nor do I think that the US navy was strong enough to keep the Royal Navy out of the Americas as well as I say, but its the only thing I can think of.
Fast Forward to the American Civil War. Britain, after the Trent Affair does decide to join the Confederacy, but France does not, so that it stays almost possible. The US somehow manages to win many battles in the Atlantic, and too many of the troops sent from England are sunk. The United States, after much hard pressed fighting on the Canadian and Southern fronts, wins the Civil War in around 1866. The Southerners, just getting used to being a nation, decide to flee to Brazil, in many more numbers than they do in OTL, which is similar to the post in the Alternate Nations Thread.
3 years later, enough southerners have fled to Brazil that they want to recreate their nation in Brazil. They revolt with British support, as they are still technically allies. Brazil crushes the rebels and their small numbers of British allies after 6 or so months. Britain, not wanting to invade Brazil and have to go through the Amazon and stuff, wishes for peace. But, Brazil does not go for it, and annexes the Falklands. Britain, fearful of more Brazilian conquests, stations its troops primarily in Africa, as its closest to Brazil. But, seeing Australia as a colony that could become wealthy and powerful, and without British troops, invades Australia. They initially take the island, but are soon after crushed.
There, not a very likely timeline, but one that fits the criteria.