With “Crossfire Hurricane” about to offer an expansive view of the Rolling Stones’ 50-year history when it opens at the London Film Festival on Oct. 18, a more fine-grain look at an important moment in the group’s early history – the rarely seen 1965 film “Charlie Is My Darling” – is about to have a handful of screenings and a DVD release.

The film, commissioned by the band’s manager at the time, Andrew Loog Oldham, and directed by Peter Whitehead, documents the group’s trip to Ireland in September 1965. The band, still performing with its original lineup – Mick Jagger, Keith Richards, Brian Jones, Bill Wyman and Charlie Watts –  had released “(I Can’t Get No) Satisfaction” as a single in Britain a few weeks earlier, nearly three months after its American release. By the time the Stones visited Ireland the record was at the top of the British charts.

Mr. Whitehead’s brief was to capture the band onstage and off, so in addition to performances, he filmed interviews with the band members as well as jam sessions, clowning around and hotel-room songwriting sessions with Mr. Jagger and Mr. Richards. The film he produced, “Charlie Is My Darling,” ran only 35 minutes in its original form, and has barely been seen. Mr. Oldham re-edited the footage as a 50-minute film in the 1980s, but it too has had limited showings....