I've just been through a few books with the following results:

From the Hammond/Gardner books:

Wanton Seed yielded 2:

The Murdered Servantman ("A famous farmer") - mrs Randall, Preston Candover(Hants) 1907
Sheffield Park - Moses Blake, Emery Down(Hants) 1906

Constant Lovers 2 versions of 1 song

Duke of Marlborough (A)William Chubb, Beominster (Dorset) 1906
                   (B)Mrs Webb, Bath(Somerset)

Marrow Bones had none


From Sharp's Collections:

Cecil Sharp's Collection of English Folk Songs (ed Karpeles)
(Letters refer to versions when more than 1 tune)

Lord Bateman E, M
Barbara Ellen G
A Sailor By My Right (Flame of Fire) (I should have remembered this-used to sing it)
Sheffield Park A
Sweet William (A Sailor's Life) B, E
General Wolfe ("Bold Genr'l Wolfe to his men did say") B
I Sowed Some Seeds A, B

Sharp's English Folk Songs From The Southern Appalachians also had none

There were several tunes that were mainly in 5/4 with odd bars of some other rhythm (for example in Sharp's English Songs most versions of The Bold Fisherman were mostly in 5/4. The Appalachians had none like this).

Mick