According to A Brief Biography of British Bikes by George MacDonold Fraser:

... In 1927 Spagthorpe introduced a model specifically designed to be ridden by the more fashionable ladies of polite society. Originally designated the "Miniature Collie," the bike became known by the more descriptive name of the "Side-Saddle."

Since it was an established fact that no polite lady would straddle a throbbing piece of machinery (in public), Spagthorpe engineers fitted a custom side-saddle seat to a 175cc one-cylinder bike. Because motorcycles are traditionally mounted from the left in Britain, the side-saddle was configured to have both control pedals on the left side of the frame. It was deemed much easier to put the shifter lever in front of the brake lever, thus the British penchant for shifting with the right foot (which would be forward while riding "Side-Saddle") was born.

In the original test rides, her Ladyship Moesha of Burkenbacksterhappenshire (a distant cousin of Lord Spagthorpe, and also a brief love interest--but that is a story for a different biography) found the balance of the ridden bike to be somewhat too "traditional" for the seating configuration. Her Ladyship never complained formally of the bumps and bruises, but she did send Lord Spagthorpe a bill for the replacement of "spoiled delicates."

Consequently, the single cylinder of the engine was placed at a forty-five degree angle from the vertical of the bike. Also, to maximize the amount of counter-balance weight created by the leaning head, a new chain-driven, double over-head camshaft design was used. This design had the added benefit of allowing the engineering of the relative timing of the valve openings to be done "on the fly" by merely skipping links on one or the other of the two cam's chains.

(The controversy over which valve opens first in a four-stroke cycle--the exhaust or the intake--would eventually tear the Spagthorpe engineering department apart.)

Introduced in 1928, the Side-Saddle mark II with its distinctive leaning head engine was a mild success in Britain. Its attempted introduction into the US the following year was a dismal failure, and led to the selling of the fabrication equipment to cover the losses on shipping costs to the US. (And thus the end of the Side-Saddle.) To quote one well-known American female motorcyclist of the time, Maggie Maythorpe, "If you don’t get to straddle it, what's the point?"

The truly sad point to consider is the oval-track racing possibilities of the Side-Saddle that were lost because of the ill-fated decision to put the riders legs on the left and the leaning head on the right of the bike. Since the vast majority of European oval tracks circle counter-clockwise this put the riders legs on exactly the wrong side for aggressive leaning through the turns. Thus, yet another chance for true British racing superiority was lost in the name of "tradition." ...

Fraser writes an entertaining overview of British motorcycles in BBBB, and I highly recommend it. I also highly recommend his biographies of Sir Harry Flashman, VC.