Charles Olson's car without reverse gear recalls another poet car, David Antin's theft-proof Sunbeam, with its backwards gearbox (shifting into first put it into reverse, and v.v.). Your correspondent's mother and family archivist reminds us of the boyfriend of an older cousin, whom we called 'Phizzu' because he wore an old FSU sweatshirt or T-shirt. He drove an old Volvo (I think) which had no reverse: he would always park where he could pull out straight.
A little on-line research uncovered the Peel P50, a street-legal car produced in England from 1962-65, with no reverse gear. The car was 134 cm (53 in) long, 99 cm (39 in) wide, and 134 cm (53 in) high. According to Answerbag.com, the P50 was not a big seller since it was very unstable, cramped, and noisy." It cost £198 and got 100 mi/gallon (take that hybrids). I guess, no reverse gear was the least of your problems. Cute though.
Peel Engineering still exists and has produced a limited number of new P50s. Here's a TopGear video of the P50 in action: