In the 1951 Alastair Sim movie Scrooge - the definitive one IMHO - Barbara Allen was played a lot, both as a theme/motif and as a party song in Scrooge's nephew's party.
Tanny wheeler, the song you were recalling is A Mother's Love's A Blessing.

A mother's love's a blessing,
No matter where you roam,
Keep her while she's living,
You'll Miss her when she's gone.
Love her as in childhood,
Though feeble, old and gray,
For you'll never miss your mother's love
Till she's buried beneath the clay.

Seamus