Those 20+ were all North Yorkshire, and none in Easingwold.
I think you have to start from basics here:
You have the birth in 1931, so you know mother's maiden name.
From that you should be able to find the marriage (using FreeBMD).
The marriage certificate will show you the father's names, and ages of the happy couple.
From that you should be able to find the family in 1911 or 1901 census.