Here's a selection of field recordings of different variants:

This version was recorded quite recently in 2016 from Molly Collins, a Traveller of County Longford, Ireland and is closely related to the version that you know from Steeleye Span, which originally came from the singing of Mary Doran, a young Traveller of Waterford, Co. Waterford, Ireland in 1952:
As I Went Out Walking One Fine Summer's Morning - Molly Collins

Here's a traditional version that has the seldom heard "Pills of White Mercury" verse, from Harry Brazil, a Traveller who was recorded in Gloucestershire, in 1978 by Gwilym Davies:
Through the Dark Arches - Harry Brazil

Here's one which actually mentions St. James Hospital.
It's sung by an Irish singer, Tom Lenihan of Knockbrack, Miltown Malbay, Co. Clare, recorded by Jim Carroll and Pat Mackenzie in 1976, although this version originated in America:
St. James' Hospital - Tom Lenihan

And here's another version which makes it clear that the cause of death is Syphillis, from Texas Gladden of Saltville, Virginia, recorded by ALan Lomax in 1941:
One Morning in May - Texas Gladden

And here's an Ohio version, recorded in 1937 also by Lomax which has almost completely lost the original story:
Captain Pearl R. Nye - Jones Hospital
The song starts at 02:50, before it is an unrelated song, Lord Lovel.

There are countless other variants of this interesting song, but those are some of my personal favourites that are easily available online.

If I may recommend a fine version from a revival singer, Tom Spiers sings "Pills of White Mercury" unaccompanied on "Tom Spiers - Allan Water (LTCD1005)".
It's a Scottish version, originally from the singer Alexander Robb of New Deer, Aberdeenshire, collected by Gavin Greig in 1906 under the title "Disordered".
It is quite graphic in terms of describing the questionable treatment of Syphillis in earlier times...