How and where would I obtain records for the Holborn Union Infirmary Archway Road abt 1881?
Unfortunately, there are no surviving patient records for this infirmary at this date.
Many patients were admitted to this infirmary via one of the Holborn workhouses. Some of the workhouse admission/discharge registers have been digitised by Ancestry in their database
London, England, Workhouse Admission and Discharge Records, 1764-1930. That might be worth a look.