Ken Garner's Peel Sessions book - the standard reference on such matters - lists a Fairport session of Sept 27, 1969, featuring Sir Patrick Spens, Jigs & Reels, Medley, The Lady Is A Tramp and Reynardine.

There's no carol service listed in 1969, but there is one listed for December 26, 1970. The only artists mentioned are The Rudies, however. Maybe that's what Peel called the impromptu band you have in mind?

Facts - I love 'em.