I think a Unified Empire State is a little ASB. The best I think you could get would be an earlier Home Rule Act, perhaps based on confederation (ala A-H and quite popular c.1900) instead of dominion/independence as a precedent
If the Liberal Unionists under Joe Chamberlain can get into government, they would have pushed for Commonwealth/Empire economic zone and Imperial Navy.
Combine these more federal moves with Indian Dominion post-WWI and strong Imperial Council (made up of British and Dominion ministers) ala the EU's Council of Ministers and I think you could get a stronger Commonwealth, combining local autonomy with international cooperation into a confederate system.
So expanded home rule to the non-white bits of the Empire in other words.
A Home Rule India would probably include the whole sub-continent, with no Pakistan-India divide.
I think the issues in Palestine would probably still exist, since I don't see this Home Rule thing working out very well vis a vis the Jews and Arabs in British Palestine.
However black Africa would probably not get anything like this pre-1950, remember in OTL the 1945 Labour govt. while leaving India and Palestine was investing long-term into Africa for military bases and economic migration.
Ya, that was the problem that Africa had with most of its European colonizers. The Europeans' African colonies were net financial losses, but the Asian colonies (I think this was the case for the Dutch and French as well as the British) were profitable, so the whole colonial venture paid for itself. The Asian colonies all had very active nationalists post-WWII, so they broke away from the European empires, and once they did the African colonies no longer looked like such a good deal. So you had very quick withdrawals from countries that were not ready to be left on their own.
If you give India limited Home Rule post-WWI, then I think that you've definitely kept India in the Empire for longer than OTL. You've also opened up the Indian economy to investment, and given a much longer lead time for the native Indian elite to decide that free market capitalism is the way to go. With British investment in the Indian economy, maybe you've somewhat solved (or at least mitigated) the financial costs that the British Empire is going to incur when India finally gets totally independent. The British will be able to continue making money in their former colony in the TL.
Also, since I don't think that this POD is enough to cause ripples that would end WWI, the rise of racist authoritarians in Italy and Germany, or WWII, this will set the West up much better for the Cold War. India will be firmly in the free market (or at least not state-run economy) camp, there will be no Pakistan (thus no Pakistan-India issues) and you have a shining example of the perks of having a good relationship with the colonial natives.
At best you might get this earlier, Westminster and the new Confederate Commonwealth investing to civilise Africa via white migration, railways, industry etc. and local limited autonomy as a first phrase to joining the Commonwealth completely
If you keep the British very involved in Africa for longer, then I think that you could potentially avoid something like the Rhodesian UDI.
What I'm imagining is a more involved Britain that prevails upon the white minorities in Kenya and Rhodesia to accept a one-man one-vote franchise. The de facto agreement would be that these governments do not have control over foreign policy or military matters (in both these areas they remain under the UK's umbrella) and since the British are remaining, these governments are not going to be able to do things like seize white-owned farms or kick all the Indians out. This gives the whites and other non-black minorities a chance to come to terms with the black majority under conditions where the stakes are lower due to British involvement.