Here's the tune from The Wanton Seed, collected by Gardiner. I've also included the three tunes from Sharp.. ed Karpeles.

Mick

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X: 1
T:In A British O' War
M:4/4
L:1/4
B:The Wanton Seed, ed Purslow
S:Collected by Gardiner from George Blake, St.Denys, Southampton, Hants. June 1906
N:The chords are as in Purslow
K:F
C/>C/|"F"F A "C7"(G/A/)(B/G/)|"F"F2 C A,|C F "C7"(E/F/) G|"F"F3
w:It was down in yon_der_ mead-ows I care-less-ly did stray;
A|A G A B|c c F c|"Bb"B (A/G/) (F/E/) F|"C"G3
w:There I be-held a la-dy fair with some young_ sail_or gay.
G|"F"A F A B|c2 F c|"C7"(B/A/) G "F"F C|"Bb"B3
w:He said, "My love-ly Sus-an I soon_ must leave the shore,
d|"F"c> A "C7"B G|"F"F C A, C|F F "C7"(E/F/) G|"F"F3|]
w:To cross the brin-y oc-ean in a Brit-ish man_ of war."

X: 2
T:British O' War
M:4/4
L:1/4
B:Cecil Sharp's Collection of English Folk Songs, ed Karpeles #136A
S:Collected by Sharp from William Lawrence, Ely, Cambs, 8 Sept 1911
N:Key signature as in Karpeles
K:Dmix
A|G F D D|G A2 (E/F/)|G F D ^C|D3
w:As I walked down yon mea-dow I_ care-less-ly did stray,
D|F G A A|d B G A|B B c B|A3
w:There I be-held a la-dy fair With some young sail-or gay.
D|F G A A|(d B) G A|B d c B|A2
w:He said: My love-ly Su_san, I soon must leave the shore
G E|D D E F|G2 A E/F/|G F D ^C|D3|]
w:For to fight for Eng-land's glo-ry in a Brit-ish man of war.

X: 3
T:British O' War
M:4/4
L:1/4
B:Cecil Sharp's Collection of English Folk Songs, ed Karpeles #136B
S:Collected by Sharp from John Dingle, Lew Trenchard, Devon, 12 Aug 1904
K:D
A|d d c d|B2 F G/G/|A A G E|D3
w:'Twas down in yon-der mea-dow Where I care-less-ly did stray,
D|E E E F|G G F A|d d e c|d3
w:There I be-held a la-dy fair With some young sail-or gay.
(d/e/)|f f d B|d2 A (F/G/)|A A G E|D3
w:He_ said: My love-ly Su-san, I_ soon must leave this shore
D/D/|E E E F|G2 F A/A/|d d e c| d3
w:And a-cross the bri-ny o-cean in a Brit-ish man o' war,
d/e/|f f d B|d2 A F/G/|A A (G/F/) E|D3|]
w:And a-cross the bri-ny o-cean in a Brit-ish man_ o' war.

X: 4
T:British O' War
M:4/4
L:1/4
B:Cecil Sharp's Collection of English Folk Songs, ed Karpeles #136C
S:Collected by Sharp from Henry Larcombe, Haslebury Plucknett, Somerset, 23 Aug 1905
K:D
d|B A (F/E/) D|(G> A) B G|(A F) E F|D3
w:'Twas down in yon_der mea_dows I scarce_ly did stray,
G|F> E D E|F G A A|d d c B|A3
w:There I be-held a la-dy fair With some young sail-or gay.
(A/B/)|G E D E|(F G) A A|d B c A|d3
w:He_ said: My love-ly Su_san, I soon must leave the shore,
B/A/|A F (E/D/) D|(G A) B A/B/|A F F E|D3|]
w:And to cross the bri_ny o_cean in a Brit-ish man o' war.