This is mislabeled on the video title.
It's really Johnny Mandel's 1955 arrangement of "The White Cliffs of Dover" from the Dave Pell Octet's 1955 Atlantic LP Jazz & Romantic Places
featuring Don Fagerquist, trumpet, Ray Sims,
trombone, Dave on tenor, Bob Gordon on baritone, Tony Rizzi, guitar, Donn Trenner, piano, Buddy Clark bass and Bill Richmond drums.