Oh! What a Lovely War. Lennon played an anonymous soldier opposite Laurence Olivier. The film is not to be confused with the 1967 Richard Lester movie How I Won the War.
The article also tells of several meetings Davies had with Lennon, and you can read the full article here.
I'm still worried that there may be a mixup of some sorts here. As you know, John Lennon and George Harrison saw Victor Spinetti in the musical ""Oh! What A Lovely War" in 1963, and subsequently recruited the actor for their first film adventure, "A Hard Day's Night". Attenborough's movie adaption of "Oh! What A Lovely War" is from 1969 (it was shot in the Brighton, East Sussex area in the summer of 1968), and the film was released on DVD in 2006.