To complete the discussion about EFDSS attitudes to collection in the 1930's, it's worth highlighting that Cecil Sharp, the founder of the EFDS and for decades the dominating influence on its approach to collection proposed that:
"the last generation of folk singers must have been born not later than sixty or seventy years ago - say 1840" English Folk -Song: Some Conclusions' (1907).
By the 1930's anyone born in 1840 would be well into their 90's. It's therefore clear why song collection was no longer a priority - or even possible from the EFDSS standpoint.
Obviously this view was incorrect, as later fieldwork has amply demonstrated. But it does explain the reason for the gap.