I don't know how reliable a yardstick this is, but last year I completed a folk song dissertation using LP and CD liner notes for source material. I analysed 300 albums covering 1958-2008, just over 3000 song notes. The songs most recorded were (in order):

John Barleycorn
Geordie
Seven Gypsies (Black Jack Davey etc.)

No surprises there, then! These were followed by (not in order):

The Grey Cock
The Flash Lad
Polly Vaughan
Just as the Tide was Flowing

Other highly favoured ones included Lord Randal, Lowlands of Holland, The Trees They Do Grow High, The Outlandish Knight, Ye Mariners All, The Cruel Mother, and Jack the Jolly Tar. The only (semi) contemporary song that was anywhere near as ubiquitous was The Gay Fusilier, and even that was way, way behind.






By the way, some of the most informative liner notes came from a certain Brian Peters, especially those for Lucy on the new CD. I've quoted you, hope you don't mind!