If the rear hub is a three speed hub, it is most likely a Sturmey Archer AW or the Hercules equivalent. If Sturmey Archer, it will have a date code such as 53 9 that translates to September 1953. If Hercules, the same date would be written "TYPE B 3"
Nothing there to suggest three speed. No shifter, no hole in axle for the tiny awesome chain, and no large drum to hold planetary gear setup.
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A race bike in any era is a highly personal choice that at its "best" balances the requirements of fit, weight, handling, durability and cost tempered by the willingness to toss it and oneself down the pavement at considerable speed. ~Bandera