Like Ian Grant said grain wise all modern 100 ASA films have less than emulsions from the 1920's and 30's. So using a 400Iso film like Kentmere 400 or Lucky SHD 400 might come closer grain wise than say Efke 100. Lucky films have a pretty much nonexistant antihalation layer, though films from the 20's and 30's had one it was less effective than todays AH layer.
Another thing is Nostalgia even using a film, camera and lens from the 1920's to 30's won't make a photograph look like it was made in this time period since the cityscape and fashion has changed dramatically and often what we like about the photos from the 30's is the fashion and old cityscape and not the look of the film.
To create a photograph looking like it was made in the 1930's you have to photograph the subject in 1930's surroundings. Old houses/streets man/woman dressed in classic clothing (e.g. trench coat or a dress made in the style of the 30's, all still available from current fashion houses)
Take HCB shot of the man jumping over a puddle this image is timeless and doesn't scream 1930's neither in look nor in fashion, one could make a photograph that looks like HCB's even today all that is required is the same foggy lighting.