I’m interested in what makes the song similar to those three songs that were posted. Two of them are in 3/4 time; the third (Eve of Destruction) is not, but shares with the others a reliance on acoustic guitar (or what sounds like it). Is your song in 3/4, do you remember?
The first song I thought of was “Nothing Ever Happens” by Del Amitri:
Also slightly similar is “Jimmy Newman” by Tom Paxton (also recorded by John Denver). I wouldn’t call it massively famous though:
There are probably thousands of songs that fit this description. It’s a style used in countless folk songs.