You need to avert the American Revolution for a start as they are not going to Rejoin post independence. Then you need to screw every other European power so Britain is the only one in the colonial game. Prussia can be knee capped with no Miracle of Brandenburg. Avoid the mass conscription of the French Revolutionary Wars and have Aquitainian and Provencal become national identities that revolt and tear France apart. At some point France and Spain can invade and annex Holland and Portugal so Britain grabs their colonies. Have Austria unite Germany but then have constant warfare with Russia to keep them busy, with both sides constantly pushing independence movements in each other's minority populations.
Have Britain keep Manila after the Seven Years War to get an early headstart in Asia. Filibusters gradually sweep up the East Indies over the next century. They replace the Dutch in Japan and end up backing various Daimyo against the Shogun. Eventually they use the Emperor as a puppet to replace the Shogun with a British resident really ruling the country. With no scramble for China, after the alt-Opium Wars they take more treaty ports, which become a whole bunch of Hobg Kongs. British forces eventually occupy the whole coast to stop other powers getting a foothold.
Britain takes the River Plate early. They take southern Brazil when Portugal gets invaded. With the economic core of the continent under British control, South America becomes dominated by British American businessmen. One by one, a mixture of gunboat diplomacy, Hawaii-style coups and economic advantage takes them into the Empire to be included in the imperial tariff system. This is extended to the North of the continent as oil is discovered there.
In Africa, Britain takes the French slave ports in the Seven Years War. It later takes the Cape from the Dutch and Angola & Mozambique from the Portuguese, during the occupation of the metropoles by France and Spain. When slavery is banned, Britain takes Zanzibar and the Maghreb to stop the Arab trade. Egypt is taken to protect the Suez. British imperial enthusiasts build a Cape to Cairo railway, which seeds settlements in the highlands of Ethiopia, Kenya and Tanganyika. Eventually, all of Africa is declared the British sphere of influence.
In the Middle East, Britain gradually grabs the hinterlands of Aden. When oil is discovered nearby, it is declared a strategic resource for the global empire. The entire perimeter of the Persian Gulf is annexed by the Brits, up the Euphrates to Kurdistan. Jewish settlement of Palestine causes much conflict and Britain moves in to protect Christians and Jews.