Political Congresses/Federations of the British Imperial Federation
United Congress: The dominant party of India, with branches present across the Empire's Dominions, United Congress remains an 'Indian' party first, with its base being the Greater India Diaspora. But United Congress has in many ways become the 'conservative' party of the Imperial Federation, defending the status quo of strong constitutional monarchy, the Imperial Free Trade Area, Dominion autonomy and Indian economic and political hegemony. By the sheer fact of being India's dominant party, having never lost an election on the subcontinent since Dominionhood in 1933, the modern Imperial Federation is dominated by United Congress - even discounting its affiliates in the other Dominions. It is notable that many of these affiliates are strong in historically white Dominions - a legacy of the 'Aryan Supremacy' doctrine that sought to press Britisher and Indian interests together against 'non-Aryan' races such as Africans and East Asians.
African National Congress: Starting in South Africa, where the oracle of Aryan Supremacy Mohandas Gandhi first elucidated his theory, the ANC has spread across British Africa. It grew into a mass movement during the darkest years of Aryan Supremacy, fighting against the union of White and Indian settlers. The final end to the doctrine of Aryan Supremacy in the 1970s was achieved by the defeat of United Congress at the Imperial elections, allowing a fragile coalition of socialists, liberals and civil rights activists to finally end minority rule. The ANC never achieved its dream of independence from the Imperial Federation - the return of United Congress to government put paid to that - but the ANC has become the second most powerful bloc in the Imperial Federation - albeit a localised one compared to the ubiquity of the United Congress.
Cooperative Commonwealth Federation: Representing the multifarious ideological socialists of the Imperial Federation, the CCF is ironically perceived as a 'white' party - the nascent socialist movement in India was coopted by United Congress, informing their technocratic/corporatists style of economics; while a similar thing happened with the ANC in that the left split on Aryan Supremacy and those opposed ended up affiliated to the ANC. This has left the CCF strongest in the older White Dominions - and in non-Indian/African regions such as Malaya.
Liberal-Conservative Federation: While many conservative parties have been coopted by or affiliated to United Congress, a great many haven't. These parties are opposed to the statist sensibilities of United Congress, their commitment to central planning, and in general the dominance of India. For this reason, the Liberal-Conservatives were once home to the Imperial Federation's white supremacists, for home Aryan Supremacy was an ideology that promised the doom of the white race. That attitude faded after the 1940s, as the ANC's struggle for civil rights grew more important, and the commitment of United Congress to imperial integrity could not be questioned. The alignment of the Liberal-Conservatives on keeping the black man down led to the more hardcore racists drifting away, and the dominance of free marketeer 'classical liberals' in the party.
National League: Technically not a Congress/Federation as that would defeat the point, the National League is the home of those who would see an end to the Imperial Federation, from Scottish nationalists, to Indian islamists, to Afrikaaner racialists. It's a sclerotic combination running a gamut of economic and social disciplines, united only by their common distaste for the Imperial Federation as an institution. The emergence of the ANC as the Imperial Federation's second party has seen the rise of National League-affiliated movements across the old White Dominions, often drawing on support that once went to the CCF or the Liberal-Conservatives.