I've only just seen this, the latest Mr Lee advert, so I don't know if this is the one you mean. The song is "You made me so very happy" and it's by Blood, Sweat and Tears.
To follow on from Cetti, it's been suggested the singer is The Velvet Fog, Mel Torme himself. 'You've Made Me So Very Happy' was written by Motown founder Berry Gordy Jr. with Brenda and Patrice Holloway and Frank Wilson. And BS&T featured the phenomenal Al Kooper on keyboards, who also plays the sweeping intro to 'Like A Rolling Stone' for Dylan.