Its caption reads in part: "Sir Roy Fedden's specially built Park Ward streamlined saloon on chassis number B189AE, registration number AXM 19, from which valuable information was compiled on reduction of air resistance and decreased petrol consumption with increased speed..."
Roy Fedden (Wikipedia entry here) was the Bristol Aeroplane Company's engineer in charge of aero motors.
Bentley was acquired by Rolls-Royce in 1931. Rolls acquired a stake in the Park Ward coachbuilding firm in 1933, eventually assuming total control in 1939.
Also during the 1930s a design fashion in England was the "Airline" style that I wrote about here and elsewhere. Those designs usually retained non-streamlined normal production front ends that were coupled with rounded-off aft ends. Those front ends considerably reduced any aerodynamic benefits the rear ends might have created.
Fedden's car Bentley 3 1/2 Litre is interesting due its design details and because it is a four-door Airline type, most Airlines being coupés or 2-door saloons. It's also a comparatively early Airline design, the fashion seems to have peaked around 1936. The car still exists, residing in Volkswagen's Autostadt museum. The museum dates the car to 1935, but its chassis number mentioned above is from 1933-1934. So presumably it took Park Ward half a year or so to create the body, completing it in 1935.
This image via Deutsche Welle shows the size of the headlights. They surely would have created a good amount of air turbulence, largely negating any front end aerodynamic features.
Another image via Deutsche Welle. Note the gap between the front cycle fender and the forward door, and that it isn't filled with a running board. Most cars of that era had S-shaped, ogive-shaped front fenders that blended onto running boards. That said, running boards are only needed below doors, so the solution seen here worked just fine. Presumably cycle fenders were used because conventional S-shaped fenders could trap flowing air in the zone abaft of the tires.
Martin Hesp photo taken at the museum. Besides the rounded aft profile, the only other aerodynamic feature seen here is the slightly raked windshield. I wonder why rear-wheel openings weren't covered by spats, a feature known at the time. They might have improved airflow a little, but creating inconvenience when wheels needed to be removed.
A Wikimedia image. Note the cutlines on the aft part of the body. Presumably they are for access to an integral trunk and/or a spare tire. Most saloon trunks in those days were either externally mounted or discrete shapes blended into the basic body form. The small backlight window is placed so high that it probably was nearly useless for driver's rear visibility (note the frontal view above and compare the backlight opening to the driver's head).