See here
http://www.theanswerbank.co.uk/Adverts/Questio n459902.html
M&S Say It's The Charioteers , but on listening to available versions the ad version is significantly different . Often bands re record songs but as yet theres no definitive answer (and the version in the ad is excellent).
Also sometimes they do a recording just for the ad.
There was a post office ad a couple of years ago . It sounded like Mike Oldfield and the promotion dept insisted it was In Dulci Jubilo (which it clearly wasnt)
At least in the case the song is right. The Charioteers version is good , the Treniers is excellent , Fat's Wallers is well worth grabiing as well