The trio are part of an all-star writing cast for the album The Performance - Bassey's first studio set in more than 20 years - which will be released by Geffen Records on November 9.
The album's producer David Arnold, who has himself co-written two of The Performance's songs, was also at the launch alongside record company representatives such as Geffen UK president Colin Barlow and selected media.
Others attending included veteran lyricist Don Black who wrote No Good About Goodbye for the album with Arnold as well as Our Time Is Now with his long-time collaborator John Barry. It is the first song Black has written with Barry for Bassey since the Bond theme Diamonds Are Forever.
Barlow has contributed This Time to the album, while Wainwright has penned Apartment and Hawley After The Rain. Tom Baxter, who was also at the launch, has written the album's opener Almost There, while others supplying songs include Kaiser Chiefs, Pet Shop Boys and KT Tunstall.