Travolta plays Danny Zuko, a leather-clad wild teenager (he was 24 at the time but his character was only 17) who becomes smitten with Sandy Olsson (Newton-John), a beautiful but "square" student at Rydell High School.
Xanadu - based on the 1980 film flop of the same name starring Olivia NewtonJohn - and Young Frankenstein beat A Catered Affair and Cry-Baby The Musical to take joint musical honours.
Mr Riddiford said that as well as family support, Kylie would be getting support from her many show business friends including Olivia Newton-John, who was diagnosed with breast cancer more than a decade ago.