Here's the entry for beginning of west part of Gooch St for 1939:
GOOCH STREET (5), 116 Bromsgrove street to 150 Belgrave road. MAP F 5 &6, G6.
WEST SIDE.
27 Priory Knitting Co. Ltd. (The), knitted goods mfrs
Corporation Swimming & Private Baths for Women (D. L. Grant, sec. & commercial. manager)
here is Kent st
One rather peculiar thing is that , if you look in the official aprt of the directory at swimming baths, it dpesn't seem to list eithe Kent St baths , or the associated Gooch St ones
Mike