Planet Earth
Hyperbole aside, with early enough and detailed enough PODs most of the world is probably possible.
Keep the rest of Europe from colonizing. A surviving Iberian Union and the reconquista continuing into Morocco would keep the two main early colonizers occupied.
An earlier Suez Canal might keep the other powers with a med. port from going to the new world. Probably want a greater Germany that includes Austria and the city of Triest in that case.
Scandinavian colonies could likely be kept sparsely populated enough to be absorbed latter.
The Dutch would likely be the other big colonizer if the rest of Europe is distracted, but an Anglo-Dutch union might be possible down the line. Or maybe the British would just 'take custody' of any colonies if the Dutch were invaded by, say, France or Germany.
Surviving as a single state depends very much on how its governed, but if the right people make the right choices at the right time, there probably is a path forward as a single state. I bet it would be massively decentralized for the longest time, but it just needs to survive until the invention of mass media and telecommunications. Again, those techs would need to be used properly to unite rather than divide, but it is in principle possible. On that note, earlier communication tech would probably be good. Even telegraph would be useful as there could be Empire-wide newspaper stories with that.
It seems to me that the Americas, Southern Africa (up to at least Congo), India (incl the Pakistans), Indonesia (incl Philippines) and Oceania (incl pacific islands) should all be doable. Also Antarctica, because who else would want it in this ALT
China is a tough nut to crack, but the British Empire described above would have a larger population and far more resources, so it might be possible. Perhaps divide and conquer during a warlord period. A sort of reverse-India. Even still, I wouldnt bet on this one.
Middle East, SE asia, and Japan all saw a fair amount of Anglo influence OTL. Some sort of 'special partnership' or protectorate status for many of the countries in those areas might be possible there.
I see Europe being treated as peers, largely left alone, for historical reasons. When the center of gravity of the Empire moves away from London, (I think the Central American Canal zone, Panama or Nicaragua, might make the best capital) that perception might change. At the very least economic domination is practically assured, unless the Europeans can form an EU quickly and effectively. To be fair, there would be a lot of incentive to do so.
Might even be able to swing a British dominated world government before the present day. You would have to set up those dominoes really carefully for that though.