The piece is called Mirie It Is. It is medieval. It is performed by the London Symphony Orchestra brass section? On the Trunk recording it is called Festival. On the Silva Screen recording it is called Festival and Mirie It Is.
These are the lyrics but in all versions this is done as an instrumental.
In Old English
Miri it is while summer ilast With fugheles song Oc nu neheth windes blast And weder strong Ei, ei! What this night is long And ich with wel michel wrong Soregh and murn and fast
In modern English
Merry it is while summer lasts With the song of birds But now draws near the wind's blasts And harsh weather Alas, alas! How long the night is! And I, most unjustly Sorrow and mourn and fast
That last line is where "Sleep close and fast" comes from when Howie is being anointed!
Director's Cut, 1:13
Final Cut, 1:05
Silva Screen, 4:49. This includes much music that is not heard in the film.