The British Empire would need to evolve into a better economic bloc and and defense alliance, a change that realistically likely predates World War One. We can speculate how a British neutrality in that war might better preserve the Empire but at minimum I think you need to butterfly World War Two.
Long term I think India is going to be independent and I think it happens before the Fifties are done in all but a very creative POD. At minimum it might be more truly non-aligned and a better trade partner. India was the linchpin of the Empire, it made the whole both necessary and functional, however one might see Persian oil shift things enough to give the Empire a second wind. Hong Kong gained importance with Chinese isolation, it was a window, but if China does not fall into communism it fades quickly, becoming more like modern Gibraltar. But Singapore might have been held without a war to dislodge the British and encourage independence, Malaya may be set on to the path of independence but Singapore if held would become the Eastern outpost, trade funnel and foothold in Asia. Persian oil still needs safe passage so the British need a basin network to ensure safe passage, this means Oman, Aden, Egypt, Malta and Gibraltar remain relevant longer. One needs a better policy in Persia to support its transition towards a real state rather than a corrupted monarchy, I ponder if it might have been enticed to Dominion status. If Persia still slips away then the British need to better exert lasting influence in Kuwait and Arabia, at least the UAE if not also Saudi Arabia. Again no WWII opens more possibility that BP and Shell are exploiting the oil rather than the American majors. And that assumes no lasting presence in Mesopotamia but that also depends on WWI just like Saudi Arabia.
Canada and Australia fell out of orbit for differing reasons but with no WWII and a stronger multilateral trade system and better coordinated defense policy they might have stayed closer. Canada could have become the door into the USA for trade with the UK offering better bilateral deals on raw materials out of Africa, Canada and Australia to placate American fears of closed doors. Africa likely stays rather "redheaded stepchild" but they got savaged by the free trade commodity paradigm too. This may get you a NATO like alliance, something akin to the EU on trade, maybe more like NAFTA. Overall a better result than how the Commonwealth seems to impact things. I will say it is not an Empire but it keeps the UK at the table.