I don't see the Imperial Federation working until much later like the 1970s this is way too early there isn't enough connectivity via technological development an you need to change a lot of minds of the British people The White Man's Burden is still the belief of most lawmakers with in Britain. you also have to avoid the first world war which destroyed any chance of the British Empire coming together
I agree - you might end up with a sort of 5 Eyes Organisation between the 5 Principle white British nations (UK, Canada, Australia, New Zealand and 'White' South Africa.)
Problem with including non white Christian 'British' is the attitudes of he day and the education of the peoples of those nations not being the same level as those 5 White nations
That being said many places in the UK are still at or near Dickensian levels of squalor.
If this federation did address those squalid issues on the Home Islands then that would very likely pay dividends in a generation or 2