It's been discussed a number of times but I think Jim McLean probably came up with the most complete answer.
"Subject: RE: wild mountain thyme
From: Jim McLean - PM
Date: 17 Feb 07 - 04:51 AM

It has been fairly well established that the McPeake's lyrics are a version of Robert Tannahill's Braes O Balquhidder although the tune is entirely different. Tannahill had two sets of lyrics, one used 'bloomin' and the other 'Highland'. There were also two tune settings by R A Smith, one to a slightly altered version of the traditional dance tune 'The Braes o Balquhidder' (various spellings) and the other to 'The Three carles o Buchanan' which is definitely not a variant of the first although I keep reading this.
Hamish Henderson in his sleeve notes to John MacDonald's Topic LP, 1974, says the air is 'The Three carles o Buchanan' but I was shocked to hear that MacDonald actually sings the McPeake's tune 'The wild Mountain Thyme'. How could Hamish make such a blunder?
I put a call out recently to see if anyone could come up with another printed version of The Three Carles ... other than that by R A Smith by to date no answer. Elizabeth Cronin also sings Tannahill's Braes o Balquhidder but her tune is different again and McColl's tune is like a slowed down version of 'Auld Maid in a Garret' which he says he got from his mother."