Use the same advanced search engine, but eliminate all options except Song Collections. Bring up the Roud Song Index and then type in your county you want to know about. Quite a lot that was collected around the country in the first half of the 20th century was published in the Folk Song Journals.

Yorkshire Collections I know of:
mine with Jim Eldon
Hudlestons
Paul Davenport
Frank Kidson
Clive Carey
Sharp, a few
Ian Russell
Ruairidh Greig
Various members of the Leeds University Folk course in the 70s.