Not 100% sure but their version is probably/possibly based on Carol#71 in the "Worral Blue Book".
It is certainly the right tune which you are looking for as opposed to the others I have checked out. #68 is the "wrong" tune as variously provided above.
I would scan it for you but my scanner became obsolete thanks to Windows 7.
The book is available from The Worrall Male Voice Choir and is excellent value for money, it contains I think 94 carol arrangements in four part harmony. They even post it to Canada, although it gets a bit pricey for four copies.
Two or three of that specific group of singers are members of Crucible and Hekety if you ever come across either of them, also Glorystrokes but we won't go there on this thread.
Good Luck JohnB.