starting out as 'popular music'
Just off the top of my head, lots more.
Sweet Nightingale, from the theatre
Dame Durden, glee clubs
Jim the Carter Lad, Music Hall
Villikins and his Dinah, theatre, burlesque
Caroline and her Young Sailor Bold, John Morgan, ballad writer
The Rambling Soldier, John Morgan
Pretty Caroline, George Brown, ballad writer
Flora, the Lily of the West, George Brown
The Constant Farmer's Son, George Brown
Bonny Bunch of Roses, George Brown
Dark-ey'd Sailor, George Brown
The Cruel Lowland Maid, George Brown
The Distressed Virgin, Martin Parker (17thc)
The Cooper of Norfolk "
John Appleby,          "
O dear O               "
A True Tale of Robin Hood "
The Wooing maid         "
Blind Beggar of Bethnal Green, Thomas Deloney (17thc)
Down in the Meadows, Thomas Wise (18thc)
The Keeper, Joseph Martin, (17thc)
The Ploughboy's Dream, William Mason,
My True Love I've Lost, Lawrence Price (17thc)
The Famous Flower of Serving Men, "
The demon Lover                   "
The Merry haymakers,             "
Johnny Armstrong, Thomas Robins (17thc)
Robin Hood and the Beggar    "
Serving man and Husbandman, Richard Climsell, (17thc)
Baffled Knight                "
Gosport Tragedy                "
No Sir No                      "
Nightingales Sing/Bold Grenadier) "

But of course the vast majority are anon.

A ggod book for which Music Hall songs were found in oral tradition is 'Songs Sung in Suffolk' by John Howson of the Veteran albums label.