Well, many major motorways and A-roads have "the old road" running nearby. Having driven down some of the bits of "the old A1", I can imagine that in the dark, with no street lights, carbide lamps on the car, little in the way of paved surfaces and with 1920s tyres and brakes it would be very different to now! Not to mention cars were still made largely of wood in very similar manners to victorian carriages, and seatbelts had not yet been invented (wasn't that SAAB in the 1940s?). No airbags either.
Also, there was no established advice on drink driving. If you read any of P.G. Wodehouse's works (which were written largely in the 1920s) you will see that his character Bertram Wooster frequently drinks himself into a stupor and drives home, sometimes passing out in the car once he gets there, and this is not depicted as anything unusual. A lot of people were probably well over the modern blood alcohol limit.
Most deaths were probably people driving into trees and walls rather than into each other.