The band whose original members had all previously belonged to the Wilde Flowers was Caravan.
Caravan formed in Canterbury, England, in 1968 with Pye Hastings, Richard Sinclair, Dave Sinclair, and Richard Coughlan. Each had been a member of the Wilde Flowers at some point, although not all served in that earlier group simultaneously. This distinction explains the wording of the question: the connection is based on individual membership over time, not one single Wilde Flowers lineup.
The Wilde Flowers were a short-lived Canterbury group active mainly during the 1960s. Their changing membership also included musicians who later formed or joined Soft Machine, including Robert Wyatt, Kevin Ayers, and the Hopper brothers. As a result, the band became an important root of the Canterbury scene despite releasing no album during its original lifetime.
Caravan developed a more progressive and jazz-influenced sound, helping define that same regional movement. Their best-known early album is In the Land of Grey and Pink, released in 1971. A common mix-up is answering Soft Machine, which also grew from Wilde Flowers personnel, but Caravan is the band whose original four members all had Wilde Flowers histories.