"this vast empire on which the sun never sets." - George Macartney, 1st Earl Macartney
The Sun Never Sets (Overview)
This timeline explores if the British hadn't involved themselves in the second world war. Although they do intervene in the first world war, they do not make the mistake of going into another one. Because of this, the empire never falls and manages to stabilize, and keep all it's post-WW1 territories. The largest empire in the world, the British have a great navy, however Germany and the US have, especially once Hitler takes over Germany, caught up to and possibly even surpassed the empire. World War II goes differently, however, no matter what, the sun never sets. The British Empire rules 1/3 of the world's land and 1/4 it's people. The empire stretches from the deserts of Australia to the arctic wastelands of northern Canada. Almost 2 billion people are today under the British Empire.
The Statute of Westminster and Dominions
The Statute of Westminster in 1931-1933 made all Dominions practically independent, however, despite this, they are classified as part of the British Empire. The Irish War of Independence (1919-1921) ended in what could be considered Irish victory, but as in OTL only lead to Ireland becoming a Dominion of the British Empire, called the Irish Free State, or the Dominion of Ireland (https://en.wikipedia.org/wiki/Irish_Free_State). Ireland never achieved full independence from the Empire in this timeline. The British also made The Raj a Dominion in 1923, following the India Act of 1921-1922. These Dominions have full control over internal (and, in certain Dominions, external) affairs.
World War II
Although Britain did not directly fight in WW2, Britain did support France as much as possible, and eventually co-operated with America to ensure France's survival. France would not collapse, however it would come very close, with Germans pushing into Paris at one point, however France managed to push back. Germany launched Operation Barbarossa as a desperate measure in 1941. By 1947, Germany had exhausted all of it's military might and Hitler had gone insane. The war quickly turned around, with the Russian push like OTL, along with a French push in this timeline. Nazi Germany would fall by 1950, ending the World War II. Hitler would flee to Argentina, much like the Kaiser fled to The Netherlands after World War I. Italian revolution would occur like OTL after France pushes into Italy. Japan would be the only successful axis power, being a dominating force in the pacific.
American Influence on Canada
Over the years, Canada has seen a shift in culture from a British culture, to a much more American one. America influences much of Canadian culture nowadays, from TV to the Radio to the internet. Despite all this influence, Canada does remain loyal to her majesty Queen Elizabeth II and the empire. American influence also played a key role on the whole empire's opinion during the cold war.
The Cold War
The British played a key role in the cold war in this timeline. The British threw their whole empire behind the American side of the Cold War. Although the Cold War is generally excepted to have had 3 sides (Democracy, Communism and Fascism), some argue it had 4, with the British Empire or Imperialism being the fourth side. Britain benefited greatly from the Cold War as the British made a deal with the Americans that if South Vietnam and America won the Vietnam war America could annex Vietnam if they promised to help defend Hong Kong, to which America agreed.
Although the empire today is more loosely united, it still exists. Although Canada, Australia, New Zealand and Newfoundland are practically independent, they still say they are part of the empire. The empire today is not how it was historically, as the Statute of Westminster made the British not directly controlling of the Empire's Dominions. Today the empire is mostly just a relic of the past, although most of the empire in Africa is still under de-facto British control. The King/Queen nowadays has no real power and is just a figurehead.