Between 1862 and 1873, St. Bride's Street was built, altering Harp Court (the remainder is seen in red) where the cholera cases occurred.  St. Bride's church (in blue) is south of Fleet Street.  The St. Bride's pump was located, perhaps, near the urinal and obelisk at the center right.

Source: Old Ordnance Survey Maps -- Holborn, The City & The Strand, 1873.