If ideas of national self-determination still influence the peace treaty, it’s very possible for it to include an independent Ireland encompassing the entire island. However, their colonies are a whole different story, since France already had what they wanted in West Africa (in contrast to Britain’s Cape-to-Cairo railway idea). Just spitballing though, Egypt could become independent as other posters have suggested. You’d probably also see an independent South Africa since it’s in a strategic location, and Italy might take over Somaliland and Kenya. However, it’s complicated to imagine how the British Empire as a whole would actually fall, and self-determination wasn’t applied in good faith to colonized peoples anyway. Ideas like Indian independence are a long shot without a bottom-up revolution by the people of India themselves and a collapse of British power allowing the Entente to support them. It’s not impossible considering there was at least one attempt at an Indian mutiny in 1915, but it’s a pretty long shot without making some substantial prewar changes.
How could the British lose so badly that they would agree to such a peace treaty? The only way I can see that happening is if somehow a huge part of their army was captured and used as hostages. Even then, the RN would dominate the access between Europe and Egypt and South Africa so totally that the UK would still have the upper hand.