I was always under the impressoion that The Cutty Wren (ans The King, as sung by Steeleye Span) was about a traditional chirstmas time celebration, where the men or boys of the village went out and caught a wren, bringing it back to the village dressed in ribbons; it may be connected to St Stephen's Day, but I believe that the origins of the ritual are older than that.

I believe it was symbolic of finding and killing the King of Winter, allowing for the sun's return. The tradition was simply incorperated in christian practises (like so many others)

Still ties in with the song you're talking about, though.