I would also agree that the reason for collapse or revolution would be pretty key to what the Empire does.
The *loyal (not SA) Dominions could well intervene or wish to do so, in case of revolution in the UK. NZ and Australia (I assume Canada too) had spent some time and effort since the South African War, in coordination with London, in building up trained reserve milita in case of war. A worried Dominion government, if the opportunity presented itself, may wish to deploy these troops to the UK (if that was possible) in support of their side/view point.
In NZ's case, the PM was Massey (Reform) who was a Irish born Presbyterian farmer, who, as WW1 showed, had a keen interest in the UK & Ireland. While he was keen to provide land to tenant farmers (his background in Ireland) he was also the face of oppression during the crushing of the left Wing / socialist Trade Unions before the war.
If there is a left wing revolt, I would think Massey would do all that he could, which may be nothing at all (given distance, potentially hostile revolutionary Navy) to intervene.
If there is some sort of Irish revolt, whether or not Catholic or Presbyterian, then he and the Liberal Leader (R Catholic Irish) may act differently. The Irish political question was a live issue in NZ at the time, although not to the degree of the UK. I note that Ward also spent a lot of time in London