The theme music from 'The Strauss Family' was arranged, and extended, for the London Symphony Orchestra, by Cyril Ornadel, and is taken from the Finale, Act 1, of "Eine Nacht in Venedig" ("A Night In Venice"). The theme appears twice in the Finale, in the song "Komm nur, liebes Kind - Mit der Wuerde", and by the name 'Lagunen-Waltz' ('Lagoon Waltz'), albeit it very briefly.
The original operetta by Johann Strauss Jr. was arranged by Erich Wolfgang Korngold and Ernst Marischka. It is available on the following CD:
"Eine Nacht In Venedig" EMI CMS 7 69363 2