My information (via Th'Antiques Roadshow), is that "Sweet Thyme" was written by both Pete Mundey (now deceased) AND John Connolly (who "wrote the chorus and changed a few lines"). Th'Antiques do a luverley 3-part version of this song! (and many others)
Pete Mundey also wrote "Take Your Time" which The Yetties recorded too. I gather Pete and John and Bill were all members of The Broadside, from Grimsby - the group being a great favourite of said Yetties ...
Cheers!