I am contemplating a non-belligerent Britain in the Great War, a thing that should do far less damage to colonialism and allow the British Empire to soldier on far longer. At bottom I believe that British political ideals will undermine the Empire, each colony will discover independence and pursue it. That said the keystone is India, it gives reason for most all the bits necessary to protect the sea lanes that lead to trade in India, gain trade in Asia or the Americas and facilitate the exploitation of Africa. The Empire can last so long as India is part of it.
Ireland is the first step in breaking the Empire, as its first conquest the Irish want independence, home rule achieved might moderate things enough to keep the remainder closer to London. But each "white" Dominion will want greater autonomy and then India and each puzzle piece follows. The only pieces that stay are those that cannot fend for themselves and why does Britain want them? Isle of Man makes sense, Zanzibar? Look at Malta, the British really do not want it. It is a dependency that made sense with British bottoms passing through Suez but as air power supplants sea power the need for foreign bases lessens. Places like Malta stop being worth the subsidy. Trade will reorient towards Europe and the Americas, Asia too might replace India, the Empire will evolve. I see a better Commonwealth.
What is kept? I like to craft a Singapore that replaces Hong Kong and is kept as part of Britain. Aden makes a good stop over for air travel, Gibraltar is obvious if only now a tax haven, perhaps Malta does get absorbed here since the Empire persists long enough to keep the trade links active? More islands, outposts and strategic bases likely get incorporated here. The big differences should be the closer linkages between the bigger pieces, the crafting of independent yet bound nations in Asia or Africa, places like Malaya.