It says a lot that a busy inner London station like Brixton isn't staffed all day and has no barriers. tfL would start the process on day one, and along with better signage and advertising, reap the rewards.
DfT let franchises are hopeless for this sort of thing in the main.
For Brixton also see Charlton, Deptford, Hither Green, Blackheath, Plumstead, Mottingham, Greenwich, Nunhead and many, many more.
Actually, the more I think the more it does seem 90% of
stations are not staffed enough or lack barriers.
At some of those stations the layout just isn't conducive to barriers, Blackheath for example, and Brixton must be one of the most dilapidated stations in the country so no chance of barriers there.