KillerT
To make the biggest and best force really needs the biggest and most powerful Britain, but also probably under some degree of pressure to prompt the military spending. [The biggest, without the best, could be achieved by a totalitarian Britain - N Korea on steroids

- but highly unlikely to be the best].
It also depends on what you assume as Britain. If you could include a commonwealth federation in which case you could have a much more powerful state.
I'm also assuming biggest and best in compared to other possible Britain's without massive tech-wanking rather than biggest in that world - say a 10,000 men British army in a world in which an insular position and much better investment in health and science meant Britain was the only state that is still in existence after a lethal world pandemic with about a 99.9% death rate. [It wasn't us honest gov

]
Given those parameters the way which gives the biggest forces without going totally ASB would involve taking down the US as there's only really room for one major maritime power and as long as Britain is a viable military and economic rival, by capacity history shows that the US will be hostile. A still powerful and hostile but weakened US would also be the best possible incentive for Canada to be included in a commonwealth federation. However Taking down the US would be bloody difficult with a 1901 POD and also need a good bit of luck so I will discard that.
Simpliest way might be a slightly earlier WWI. If say even a couple of years earlier, say coming off the 1st Balkan war or the 2nd Moroccan crisis. This has a couple of advantages. I think the French hadn't adopted Plan XVII at the time so their more likely to have a head-to-head clash on the Belgium border which will be very expensive for Germany compared to OTL. Also the Haber Process won't have been as advanced at the time.
Hence the war ends relatively quickly, say late 13 or early 14 with a limited German defeat and much lighter losses by all involved, especially Britain which is still in early stages of mobilising. At the same time it shows up some of the military, economic and industrial shortcomings and prompts their resolution.
America still launches it's huge 1916 naval programme, prompting the Japanese response and after a short delay the British one. Britain has learnt most of the lessons from OTL WWI and is in a much better economic condition. Hence, once the US refuses suggestions of a conference to limit naval forces Britain responds and also concerned about the US programme and wild talk by some politicians the alliance with Japan is renewed.
...
Ideally there would be some federation of the white dominions and probably some key areas such as Singapore, Malta, possibly Malaya as a whole and continued influence in the Persian Gulf but most of the empire is given independence, somewhat more orderly than OTL.
Occasional tensions in Europe and America keep military investment pretty high and in the last few years tension has risen in both areas, meaning that an arms race has developed and hence force sizes, especially in the navy, the air elements of the naval and army and the space forces are expanding.
Steve