The American Revolution is averted with some sort of standing committee which evolves into an Imperial Parliament over the years. During the Napoleonic Wars Argentina, Malta, Corsica and Hanover are formalised as part of the British Imperial Commonwealth.
The British-Mexican War fought in the 1830s sees Mexico become a number of Dominions. Britain slowly extends its influence over the Carribbean and takes the Spanish Empire in the British-Spanish War. A British sense of Manifest Destiny is fostered but for the entire world.
The Scramble for Africa sees Britain take the lion's share of the continent and Afghanistan is annexed to British India. Meanwhile Germany remains divided and China sufferes a complete breakdown, which allows Britain to expand its reach in a Dominion of Canton(?).
The Great War between the Franco-Austrian-Spanish alliance and the Russo-Prussian alliance lasts six years and ends in a draw, with the continent devastated. In the 1910s Britain intervenes during a war between the Ottomans and Italians, turning the Ottoman Empire into the Dominions of Mesopotamia, Arabia and Anatolia.
A nationalist german uprising unites Germany, and the country allies with Russia to conquer the entirety of Europe. Britain involves itself late, allying with the Iberians and Scandenavians against the Russo-German-Italian alliance. By the end the Dominions of Siberia, Sardinia, Sicily, Westphalia, Poland and Brandenburg are established. The destroyed states of France, the Low Countries and Balkan States see the same treatment.
At this point the Emperor/Empress of the British Imperial Commonwealth invites any ruler to swear fealty as Governor or Vassal-Monarch or risk being locked out of an exclusive trade zone. This sucks in all except East Asia by the late 1900s. Japan never modernised so when a British delegation is killed in a misunderstanding the island is seized and incorporated by force. After this China, never having entirely reunified after its collapse and desperate for economic aid, swallowed its pride and joined the empire. In 2007, the first Imperial Astronaut lands on Mars.
Stupid, unrealistic and far from proof-read but I had the idea in my head and thought I'd jot it down. Either that or a 14/1500s expansionist China get my vote.