Do you know who played which parts on this recording? We know that Tim Rice played the Elvis-styled Pharaoh, but am I right in saying that David Daltrey took the part of Joseph?

Yes correct. Everything else was sung (mostly as naration) by members of a group called "The Mixed Bag" and/or by the childrens choir that originally sang the cantata version.

The part of Joseph was performed by David Daltrey of psychedelic EMI recording group Tales of Justine. He was not part of the Mixed Bag group, but they were all friends from the Potters Bar music scene. David Daltrey was managed by Tim Rice and Andrew Lloyd Webber at the time, and fellow EMI colleague Martin Wilcox, also from Potters Bar, suggested the Mixed Bag to Tim Rice to help out as a backing group on the Joseph album. David Daltrey sang the part of Joseph and also played lead guitar on the album, which fared better in the United States of America than it did in Europe and the United Kingdom. The original Joseph started out as a pop cantata, and over the years has developed into what has arguably become one of Rice and Lloyd Webber's most successful musicals. The original Joseph Consortium LP with Daltrey as Joseph, is still a highly regarded version in its pop cantata form, and it was also issued on CD. Daltrey was 'released' from EMI under a special one-off contract to Decca Records, enabling him to record the Joseph album. Tim Rice appears on the LP in a cameo role as the Elvis Presley styled Pharaoh, and other parts, mostly narrative, are performed by members of the Mixed Bag group, and the choir of Colet Court School.