This post is based on another snippet from the Kent Route Study, which you can download from this page on the Network Rail web site.
The study says this about the possibility of reopening East Brixton station.
5.15.17. There was a station at East Brixton on the rail route between
Denmark Hill and London Victoria which closed in 1976. The station
site sits within the London Borough of Lambeth.
5.15.18. As with Camberwell, there have been numerous calls from
local stakeholders to reopen the station over the years. The London
Borough of Lambeth is keen to reopen the station to improve the
connectivity of Brixton town centre to orbital rail routes, building on
the success of the London Overground route to Clapham Junction
which opened in 2012. If reopened the station would be served
solely by London Overground services operating to and from
Clapham Junction via the East London Line.
5.15.19. The London Borough of Lambeth are therefore leading a
review of the business case and demand for East Brixton station
with support from Transport for London and Network Rail. This
review will include consideration of the impact of a new station on
local development opportunities. It is expected to complete during
early 2017 and will determine whether or not the station has a
viable business case. Any further developments will be reported in
the final Route Study.
If you look at this map from carto.metro.free.fr.
East Brixton station is clearly shown on the tracks now used by the East London Line.
These pictures show the railway and what remains of the station on Moorland Road.
This Google Map shows the location of the station.
Note that the venue; Brixton East 1871 is shown in the pictures and on the map.
In an ideal world Loughborough Junction and Brixton stations should have platforms on the Overground, but budgets are not limitless, so neither of them has.
It may look a stiff climb to the platforms, but it is no more than some other Overground and DLR stations. Lifts would be essential.