Apologies if I've pointed this out before, Richie, but the early 19thc broadsides don't appear to have had any influence on British versions. The common widespread broadside printed by Pitts has 2 of the earlier stanzas shunted into one stanza and this stanza is not found in this way in British oral tradition according to a study I did quite some years ago. The same stanza is in the Madden copy referred to above.

It runs
'Nothing but death is painted in your face
All joys are flown from thee
I cannot save thee from the grave
So farewell my dear Johnny.'

Just to be sure, I'll have a quick scan through Bronson.

At a guess I would say many of the British versions derive from well-known anthologies and the various sheet music versions that were circulated in the 19th century.