A Labour government would be an improvement on a Conservative government, offering competence and probity. But such a government would not be economically radical and might erode liberal democracy.
For the answer to ‘How would British Labour govern the UK?’ I would imagine a good starting point would be to look at the one British country where Labour is in government - Wales.
The pragmatic moderation on display from Welsh Gov would neatly align with a Starmer-led Anglo-UK Gov but might chafe with a Scottish Labour Gov, should that ever come to pass.
What a choice though. Less corruption and venality, plus a bit more redistribution, while denying the existence of biology or the right to voice opinions that the majority of people hold.