St. Mungo’s Hospital is founded by Mungo Bonham

The hospital was founded to cater to the unique medical needs of witches and wizards, whose ailments and injuries would baffle a Muggle doctor.

The original location is unknown, since presumably Purge and Dowse Ltd., the abandoned London department store that now houses the hospital, did not exist in the seventeenth century.

Timeline Notes

Bonham lived from 1560 to 1659, which means that the earliest he could reasonably be expected to accomplish something like this is the 1590s. It's reasonable to assume that he founded the hospital early in the 1600s around the age of 40.