Were they unified on racial policies? Were they culturally integrated at all? As the white minority did the English-speaking South Africans have any real power once South Africa became independent?
I mean these are just some questions that someone could answer but the truth is is that I have close to no knowledge about this at all.
Perhaps a few snippets about the last really apartheid prime minister and president, P.W. Botha, might make a good example.
On the one hand... Afrikaners remembered being put in concentration camps by the British (as was P.W. Botha's mother) in the Boer War, and there was a certain sympathy for the Axis among Afrikaner groups like the Ossewabrandwag during WWII (in which P.W. Botha was active).
On the other hand, his second wife's name was Barbara Robertson. She was born in Britain.
(Anecdotally: I grew up being told there was a thing for a while in which British colonials sent their pregnant wives "to the home country" to give birth on British soil - it's why my grandfather was born in Edinburgh and not Johannesburg, where his father had already set down roots. I don't know if this is Barbara Robertson's story or not, but I mention it as a cultural note that might reveal something about Britishness and South Africanness.)
Anyway, P.W. Botha first studied law at Grey University College, named for a British governor. At the time Botha was there, 1935, a "Grey Boy" was also a prominent rugby referee, "Gubby" Barlow - full name Herbert Brereton Randle Barlow - who, in turn, might have played cricket under one of the school's more notable masters from a generation prior, Alfred Richardson.
So on your second question, yes, they were culturally integrated... to a point.
To your third question, yes, there were notable and influential politicians among English-speaking South Africans, especially in Natal Province. Here's a list of the mayors of Durban, for instance - either the second or third largest city in South Africa. Note a distinct absence of Van Der Merwes and du Toits among the names....
At the time Botha gave his famous Rubicon speech, I believe the mayor was Stanley Lange.
(Anecdotally again: my same Scottish-born grandfather served on the city council of Pietermaritzburg. Even in failing health during the waning years of apartheid he refused to stop standing for his seat because he didn't want the National Party - P.W. Botha's party - to gain one. The Nats tended to be more Afrikaner, the Progressives more British.)