The words seem to come from the 17th century and there are a couple of slight variations out there (Also known On Christmas Night True Christians Sing). The tune 'Sussex Carol' was written down by Ralph Vaughan Williams after hearing someone sing it in the English county of Sussex. This recording uses his arrangement from The Oxford Book of Carols.
This is another one I recorded last year and never uploaded - don't know what happened I seem to have loads of stuff from last December - strange!