Picking up on points I +still+ seem to have missed:

Guest says:

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Robin, the Lock Hospital was (I THINK) at the illustrated site from 1764 to the 1860s, so fits the postulated time ranges.
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Sorry, I jumped over this. I'm sure you're right that the image of Lock Hospital is +the+ Lock Hospital, but 1764 simply gives a +terminus ad quem+ -- the bloody (unbloody -- doesn't turn bloody till he's gut-shot in Laredo)Unfortunate Lad could have been outside it anytime between 1764 to 1860.

(And as yet +another+ query, is he outside it because he's been kicked out to free a bed, as he's terminal, or have his buddies just stuck him there? Prolly not that important.)

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The only Bodleian broadside with a suggested date (1863-1885) is not reproduced by them.
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Sure? My reading of the Bodleian site is that the 63/85 dating is linked to the two Such printings, one of which +is+ scanned. Masato gave a clicky to this earlier.

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Echoing Malcolm, one printer, Masran, used a frame around many sheets that showed blackface minstrel characters on one side. The lyrics could have been about a Scottish lass or whatever. Blackface minstrels were very popular in the British Isles ca. 1850-1900. Any illustration helps catch the eye of the consumer.
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This is fascinating -- I was a bit gobsmacked by the blackface in the broadside. This explains it. (I'd always assumed blackface located in Al Jolson -- more fool me.)

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I found one reference to "The Trooper Cut Down" (I have lost it, and not the version in the DT) that gave the date 1780 and said it was the ancestor 0f all the Laredo-Pills of Mercury-Unfortunate etc. etc. lyrics. Probably not.
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Undoubtedly not. (I'll come back on this.)

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Having done some genealogical work, tracing Capt. Townsend is a long, long shot. Royal Naval records are quite good for officers, but not so good for the "foot." The name is not uncommon and is probably invented anyway.
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Concur. Except I'm being bugged backchannel not to give up on this. And narrowing the time-range helps. But this is WAY outside any expertise I have -- anyone based in London have easy access to the Public Record Office?

Guest continues, on "The Trooper .." ...

ME: This has to be later. Two points. An intrusive moralising stanza:

O mother, o mother come sit you down by me
Sit you down by me and pity my plight
My body is injured and sadly disordered
All by a young woman my own heart's delight.

... and that fascinating term, swaddy/squaddie:

    "Here comes that young squaddy whose money we squandered"

I've hit on two transcriptions which use this term -- the other has the term "boondooks", which (to cut a tale)suggests that this version locates in the Boer/South African war of 1905.

Also the flash girls (thus termed -- originally gallows-whores)comes in about then. All-in-all, The Trooper is later ...

Malcolm said:

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The set GUEST refers to, as quoted by Masato, is not traditional, but is a modern collation put together by Stephen Sedley for his book The Seeds of Love, published in 1967. Sedley provided two tunes; one noted by Hammond in Dorset and the other by Sharp in Somerset; both in the first decade of the 20th century.
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James Reeves, _The Everlasting Circle_ (1960)provides two texts, "The Sailor Cut Down in his Prime" and a girly version, no title, beginning, "As I was a-walking down by the seaside". Reeves was using texts selected from the Hammond, Sharp and Gardiner notebooks.

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The text was, to quote him, "collated from a broadside, Hammond's and Gardiner's manuscripts and the version sung by Harry Sladen of Manchester.
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See above.

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That is to say, the song; not the form in which he published it. The internet is full of inaccurate or incomplete copies of published material, often placed there by people who have taken at face value things which they have found in books (sometimes without taking the trouble to read the accompanying notes, even where such exist) and, unless a specific source which can be checked is referred to, such things cannot be considered to be of any importance so far as the consideration of the history of a song is concerned.
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Say that again, thrice. The only primary text I'm even remotely sure on is the Bodleian versions of the Unfortunate Lad.

But it's not just NetWorking that you dead-end on this -- Holloway and Black don't document their source for "The Buck's Elegy". Neither does Root&Branch.

[sigh]

So, where are we? Up the proverbial without a paddle.

I've carved a few days in London next week, when I'll be able to chase stuff in the British Library. At the moment, I'm stuck on secondary material to follow-up, so any suggestions on Things To Look At would be gratefully appreciated.

Also, I've a long write-up (changing by the minute as I feed-in the marvellous material that I've been given in this thread that I hadn't encountered before) on Rake/Laredo generally. It's a bit long to post, but anyone who'd like to see it, mail me, and I could backchannel it as an Attachment.

Robin