I'm finding this conversation about 'community' and branding and that a bit jarring tbh.
That building is obviously prominent and important. It was the Railway for 100 years or more and formed a centrally important part of Brixton life. Certainly in its latter years it was for all sorts of different groups who rubbed shoulders and drank in there, in the days when the local was a very important part of communication rather than simply for socialising amongst peers.
Then for whatever reason it metamorphosed into a trendies pub and changed its branding to reflect that, in much the same way the Atlantic became the Dogstar, the Canning turned into whatever its called now, the Hope... and so on, all aimed at much the same, rather narrow, demographic, part of that phase of gentrification.
Then a very few years later it was gone, that incarnation as fleetingly irrelevant as (I had to look this up) Babushka. Except to 'the community' as represented hereabouts, for whom 'Bradys' seems to have mythological status as an exemplar brand of some sort.
None of which matters, of course, but maybe some perspective could be applied when getting precious about these things.