The Society's exterior is based largely off the Royal College of Surgeons in London. I mainly chose it because of that whole "large stately government building" look, but it also happens to house my favorite museum in London, The Hunterian Museum!
The Hunterian was started from the collections of the great 18th century anatomist, John Hunter. His cabinet of curiosities included such treasures as two-headed babies, two-bodied goats, and an entire human nervous system slapped onto a block of wood. A block of wood! It's not for the squeamish but it is a marvelous place for history of medicine nerds. It also looks super friggin cool. Check it out!
John Hunter also happens to be one of the original inspirations for the character of Dr. Jekyll! R.L. Stevenson's design of Dr. Jekyll's house--a respectable home out front, a spooky laboratory out back--is largely based on John Hunter's house. Hunter lived during those wacky Enlightenment years, back when they called scientists "natural philosophers" and only rich guys could afford to study science because it wasn't considered a "real job" that got a "salary". There weren't many laboratories where he could stash all his crazy science-y stuff, so he basically stuck it all in his second-house behind his normal house. So, yes, mullet house is based in historical fact.