The dance has been variously identified as the Lindy Hop, the Big Apple, and the Charleston, while the two dancers are Al Minns and Leon James. Enjoy!!
"Terry sez, Contemporary swing dancers sometimes dance 20's Charleston and Balboa to hip hop. Those styles also go great with bhangra. If you're interested in swing dance footage, there's over 30GB of vintage and contemporary swing dancing clips at dans.poy.no."