Update: Chris Corner explains that Back St. Hilda's Terrace used to be lined with stables and carriage houses for the well off inhabitants of St. Hilda's Terrace itself. Being rather well fed and possibly a bit rotund, the residents would need all the help they could get to mount their horses.
St. Hilda's Terrace was originally known as New Buildings, and there seems to have been an attempt to change the name to King Street at some point. An inscription on number 14 gives a date of 1779. It is a row of 25 houses which display a considerable variation in size and layout.