I read Mustard's thread on a British superpower in the wake of the 2nd WW. I thought a bit and taking a PoD of the end of the Boer War, came up with this very rough sketch of a timeline.
1901: The British government recognises the critical future importance of the Dominions contribution in maintaining British power. Thus they begin to cash in their investments in the US and rather than spending them on high explosives to throw at Germany, they invest them on developing the Dominions' and India's industrial base along with modernising British industry.
1911: The third Irish home rule act is introduced a few years early and thus not scuppered by the 1st WW. After some rather tense teething problems, an Irish civil war is avoided and home goes relatively smoothly despite some very loud grumblings from nationalists and loyalists.
1915: Rather than trying to run a full scale continental land and naval war, Britain scales back it's contribution to France and concentrates on Gallipoli and the Balkans. A bit better management opens the straights and keeps Bulgaria out of the war.
1916: Due to greater Entente support the Brusilov offensive is a greater success and the Romanian oilfields stay out of Central Powers hands.
1917: Despite some very serious speed wobbles Russia stays in the war and while the US stays out (lack of diesel prevents USW), their cash (in the form of unsecured loans) comes in. The war comes to a close with a negotiated CP defeat at the end of the year.
1919: The policy of Indianisation introduced in the wake of the war is more extensive and effective than in the OTL. The prewar policy of industrialising the Empire is continued and expanded.
1922: The success of Irish home rule has lead to calls for similar in Scotland. In a revolutionary move power in the UK is devolved to to the three kingdoms (England, Scotland and Ireland; sorry Wales misses out yet) and the Westminster parliament is changed into a body governing matters that affect the entire country, along with directing the Empire.
1930: Rather than the Statute of Westminster setting the Dominions on the path to independence, it transforms the Westminster parliament into a full Imperial parliament by extending representation to the Dominions. (Wales gets it's own devolved government about here).
1934: India is granted a form of home rule (possibly patterned on Irish home rule). Eventually this is extended to a full Dominion status with representation at Westminster in the wake of the (highly butterflied) 2nd WW.
Thus is created an industialised Imperial Federation. Comments, suggestions, rotten fruit and vegetables are welcome.