Following the post-war baby boom, and a burgeoning prosperity in the West, the 1960s were awash in cars as well as enterprising young people. It was almost inevitable that the practice of phone booth stuffing (remember phone booths?) gave way to car stuffing.
At the time, the favourite car to stuff with people was the VW Beetle. And the Morris Mini. Around the same time, concern about world population - or rather, over-population - began to surface among the general public. Maybe being immobilised over the steering wheel by the bodies of friends made people think.