The excellent YouTube channel, Collegium Regale, has the music from this years Carols from King's up in playlist form here. (Unfortunately there are ads.)
In several past years, this channel has the complete Carols from King's up. I hope it will do so again this year. But having just typed that, I think found the complete Carols from King's 2015 at the VoicesChoral channel.
Remember this is the made for TV program with a different format than the live Christmas Eve Nine Lessons and Carols service on radio. (Trust me I could be more critical, but I will relent this day.)
Enjoy and have a Happy Christmas.