As an Indian woman who moved to the UK in adulthood, I've been bemused by the concept of being 'politically Black' or 'political blackness'. I could never envision calling myself 'Black' for any type of political and socioeconomic struggle as to me it would feel deeply disrespectful of the unique historical issues faced by black people in general.
A few years ago I became aware of a fascinating side of British history whereby people from African, Carribbean and Asian heritage came together under the label of Black to mobilise and fight for their rights as a minority group. It's a shame that there is so much blind swallowing of Americanised cultural ideas these days, that interesting historical developments in Britain are obscured.
This is a long article by Rahila Gupta, but I found it very interesting. It charts the rise of this concept of being politically Black but also follows its disintegration over time.
newint.org/features/2020/10/06/long-read-political-blackness
The article also looks at how feminist movements were organised around this idea and I will post quotes from the article here because that's why I thought to start a thread in this board. I'm sure there are women here who have knowledge of this area, so it would be interesting to hear your perspectives. 
The Organization of Women of Asian and African Descent (OWAAD), set up in 1978 by African women, was the first black women’s organization of which I became aware. An unnamed member of the Brixton Black Women’s Group, writing in Feminist Review (FR), described her surprise when 250 women turned up to its first national conference.
They had no idea of the appetite for political organizing on the ground. It was the women who attended that conference who went back to their local areas and set up Black Sisters organizations around the country – Camden Black Sisters, Liverpool Black Sisters, Birmingham Black Sisters and so on. It did not matter what their internal composition was, or which ethnic group dominated, because Black was accepted as an organizing principle. Only one survives today: Southall Black Sisters (SBS).
OWAAD organized a protest at Heathrow Airport against the virginity testing of Asian brides by immigration officers to assess whether their marriages to British spouses were genuine (based on the state’s stereotyping of Asian culture in which women were always virgins at the point of marriage) and against ‘sinbins’, a shorthand for the exclusion of African-Caribbean boys from school.
Despite mutual support for each other’s struggles, OWAAD closed in 1982, unable to deal with ‘the complexities of putting the political principles of Afro-Asian unity into practice’, according to the FR article. Even the understanding that colonialism had divided the Asian, African and Caribbean peoples into ‘coolie’, ‘savage’ and ‘slave’, as Sivanandan put it, did not save them.
There were tensions between women who were involved with liberation struggles on the African continent and Caribbean women who wanted to focus on issues of racism in the UK and, although they knew that the two struggles were connected, they were unable to come up with a practice that accommodated both. They were reluctant to address the issue of cultural differences with Asian women because they were focused on unity, afraid that it would prove divisive and unable ‘to grasp the fact that recognition of cultural differences can be a political strength’.
Those who pushed for separate organizations in the 1980s argued that Asians and ‘Afro-Caribbeans’ (the label then in vogue) faced different issues: Asians were up against immigration laws and the Caribbean struggle was about black boys underachieving at school and being overrepresented in the criminal justice system.