Sturmey Archer was a subsidiary of Raleigh during that time period, so Raleigh Sports/Superbes were made specifically to fit SA hubs. Notice that the axle is made with milled flats, these fit matching dropouts in the Sports/Superbe. Sturmey Archer has maintained a remarkable continuity, one can get direct replacements for parts separated by 60+ years. The upshot is that yes, modern hubs will fit into the dropouts exactly without filing, as originally designed.
That 10.3mm(13/32") axle diameter is for the SA specific axle nuts. The 8mm (5/16") is the distance across the flats.
The only time you have to do filing to the dropouts is when fitting a non SA hub that has an axle that is either not 5/16" in diameter, nor has flats of that diameter.
Are you putting in an new production AW or an SRF3 hub? Those still come in 114mm OLD, and those models listed as having larger OLD merely have a longer axle that is spaced out.