Thanks Mike for that. I thought it was a bit odd that the Dispensary gets no mention in the directories so I've been digging around. This extract from Langfords: A Century of Birmingham Life in 1868 says:
"This laudable institution originated around a select society, and was carried on in a private manner for some time; until they were joined by the late Matthew Boulton Esq. who took it under his patronage in the year 1793, when a house was taken in Temple Row, and an establishment formed; he taking it upon himself the office of treasurer, saying "if the funds of the institution are not sufficient for its support, I will make up the deficiency". It continued in Temple Row supported by voluntary subscriptions and donations until the year 1808"
So it had left Temple Row by 1808. In that case either the drawing is a much earlier drawing or was drawn retrospectively. The Dispensary then moved to new premises in Union Street in1808. Interesting too that there was a Boulton connection.
Rupert thanks for the interesting info. Nice to find out that the stable area might be Bradford Passage. The NW Arcade, although still there, is nothing like the original. I worked in an office above Rackhams and, from memory, the Arcade was a very cold and draughty place, but maybe it's been improved since I last saw it. Viv.