Right, here we go. Holloway and Black. These are not the only ones related to folk songs in the 2 volumes but just leafing through, what I can see immediately
1 Admiral Benbow (Come all you sailors bold version)
6 The Black Cow (trad in Ireland I believe)
11. Bold Captain Avery
17. The Buck's Elegy (Young sailor cut down)
18. Bunch of Rushes
36 The English Rover (Roving Jack of all trades)
37 The Bold Lieutenant
41 The Fishes (Up jumped the Herring)
46 the Highwayman Outwitted
54 the Irish Lovers (The winter it is past)
66 The Lamenting Maid ( "   "            )rewritten
71 the Maid and Wife
76 The Maids Resolution to follow her Lover (Polly Oliver)
77 The Merchant's Courtship (string round her finger)
80 Mountains High (Renardine)
88 Harry Newell (Hexamshire Lass/Katy Cruel)
90 Patrick Flemming (Whiskey in the Jar)
91 Paul Jones
94 Lark in the Morning
95 Sprig of thyme
99 rakes of Stony Batter
102 Riley and Colinband
108 the Grey Cock
109 Skewball
111 the Sheffield Apprentice
123 Will the Merry Weaver
127 The Young Man's Fortune (When I was a little boy)

That's 27 just in the first volume and whilst leafing through i came across several eminently singable songs not on the list above.