You make a recording and find someone else has just beaten you to it... However;
St. James Infirmary has its origins in an 18th Century Broadside called "The Bucks Elegy". It appeared many times in Broadsides during the 18th and 19th centuries always with the same story of someone struck down with an ailment which, reading between the lines, was most likely syphilis - regular reference to pills or salts of mercury is the clue. It crossed the pond as The Streets of Laredo where the ailment was a gunshot wound and also wound up in New Orleans as St. James Infirmary but by this time the story had become vague. A constant feature apart from death was the request to be buried with what amounts to full military honours or something very like it and that is a remarkable constant of all the versions of a series of songs collectively known as the Unfortunate Rake or the Rake's Lament.
Paul has suggested that St James Infirmary was in Westminster. The Bucks Elegy refers to Covent Garden which locates the song in London, so St. James Infirmary could well be the Westminster version. About the same time as the Buck's Elegy, the song was known in Dublin as the Unfortunate Lad, though Irish versions at that time were more fragmented. Another version I have refers to The Lock Hospital which someone suggested might have been in Liverpool. Perfectly plausible given Liverpool's status as a port and the song could have crossed the Irish sea from there as the evidence, such as it is, is that the Buck's Elegy is the earliest version. Somehow the reference to St. James Infirmary got lost in some versions but not in others. The perigrinations of these songs is not always easy to tease out even with the evidence of publication as Broadsides were rarely dated.
There have been many recordings of this song over the years but for me, Louis Armstrong's 1929 version with his Hot Five is a classic.