Based on the detail of the black piece pulling the indicator chain It could be a Sachs 3 by 2 hub.
that piece is made by Sachs ( though sold separately It is one thing easier to take loose when you have to mend a Puncture)

If you can look at it in Closeup .. the Sachs Driver uses the same 3 spline driver as the SA 3 speed, just wider for 2 cogs 13 & 15t.

[I have used the 3/32" skip tooth 15t in my 3 speed _ 1 tooth in 5 is shorter to ease shifting to the 13t.]

the Sturmey-Archer (sun race) hub uses A 9 spline driver pattern , standard adopted from Shimano.
( Its used on their S3X, and spline got threaded .. Freewheels screw on the fixie 3 speed)

Of course if that close the hubshell will read BWR on it.