In a building of the age of 221b Baker Street it's unlikely that it was overhauled to allow the necessary plumbing for indoor toilets.
Around 1900, rich men might not have toilets either. What they did have was servants to take out the chamberpots. Said chamberpots might reside in a wooden arm-chair, where the bottom part was enclosed (with a front door, a mini-cupboard, if you will), and the seat would have a manhole-like cover, of the same wood.
In the country (and perhaps not only), chamberpot contents would go into the manure pile. Which might be under an outhouse with a similar seat arrangement.
The stories start in 1887, interior flush toilets were something of a luxury at the time, having only been popularized two years prior (by a guy called Twyford).
Houses that already existed did not have room for a 'privy' unless they were extensively remodeled (a toilet needs a lot of plumbing).
If there was a toilet it was most likely on the ground floor, near the front of the house (to economize on the runs of big diameter pipes).