The Dunster Lullaby, as sung by Coope Boyes & Simpson in their Christmas Truce performance, is a lovely gentle song. And I'm sure we could claim In the Bleak Midwinter as folk - Holst could well have plundered some of the tune from a traditional source.
There's some good Christmas songs by the Susex a-capella group Ramskyte on one of their CDs, and Maddy Prior ands the Carnival Band did a good Christmas recording some years back. All infinitely better than anything by Max Bygraves!