The British have a lot more success during the War of 1812, which allows them to prevent American expansion and gives the British clear control of the Oregon Country, perhaps even a few parts of the Louisiana Purchase. During some early 19th century war with Spain, the Brits are extremely successful and grab massive chunks of South America including Argentina, Paraguay, Bolivia, Uruguay, and Chile as well as the Philippines, Cuba, Florida, and Puerto Rico. When Mexico balkanizes, the Yucatan pleas for help, which the Empire is more than happy to give it.
The Empire annexes Greenland, Iceland, and all the Virgin Islands at some point, just to make itself feel powerful. Later, Russia gets tired of its good-for-nothing, money-draining, barren wasteland in North America and sells Alaska it the the British for a decent price (better to get some cash from it than lose it in a war). Italy never gets a foot hold in Africa after the Brits flatten Ottomans and take control of the oil rich Arabian peninsula. That solves the land problem. Then, another war against Germany turns particularly sour for the French and the Dutch, so the French and Dutch colonies join the Empire (directly in the case of Dutch Indonesia and Madagascar, or indirectly, like some sort of defense union, for Algeria and the like) for their own protection.
To top it all off, the Brits send an expedition to Antarctica and claim the land in the same of the Empire to show that the Sun truly never sets on the the British Empire, which now spans from every sea to shining sea as well as pole to pole.