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It was also not written by Robert Burns, although this error seems to be becoming more frequent since Eddi Reader included an unrelated song (also not written by Burns) called “Wild Mountainside” on her album Eddi Reader sings the Songs of Robert Burns.
Wild Mountain Thyme (also known as "Purple Heather" and "Will You Go Lassie, Go") is not even a Scottish song. It was written by the Northern Irish singer Francis McPeake, who first recorded it for the BBC series "As I Roved Out" in 1957. As he had already taught it to others by this point it must have been written some time prior to 1957. There are two versions of how it came to be written. According to “Ireland the Songs, Volume 2, pub. 1993, Walton Music Inc.” he learned it from his uncle and wrote it down, but according to Eric Winter, in the liner notes of the 1995 re-release of The Corries: In Concert/Scottish Love Songs,
"Francis wrote this version … and dedicated it to his first wife. Long after she died, he married again and his son, Francis II, wrote an extra verse to celebrate the marriage."
Both stories are probably true as the song is based on an earlier Scottish Song The Braes of Balquhidder by Robert Tannahill (1774-1810). This earlier song includes the lines "Let us go, lassie, go" and "And the wild mountain thyme". It is entirely possible (probable even) that McPeake learned this earlier song from his uncle and turned it onto the new song. The tune of Wild Mountain Thyme is completely different and unrelated to the older song.
Here's an interesting website with more info: http://www.ecalpemos.org/2011/08/origins-of-song-wild-mountain-thyme.html