The synth-pop duo has teamed up with Martin Meunier, who helped director Tim Burton create his stop-animation characters in James and the Giant Peach and Coraline, for the promo.
In the video, Bell and Clarke's animated doppelgangers perform the song made famous by folk group Steeleye Span as hooded monks in a roofless and forgotten church on a snowy Christmas night.
The track is the first single from the duo's new Christmas album Snow Globe, which is released on 11 November (13).
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Falling For You is the new single from German house producer Teenage Mutants, the track features vocals from Brit Laura Welsh.