Here to prove you can never have enough documentaries about Muhammad Ali is New York director Muta’Ali Muhammad, who has made a new film on the subject for the US’s Smithsonian Channel; it is entertaining, but perhaps unsure of what exactly it’s saying that is new. It focuses on the legendary boxer’s public life from 1959 to 1964, as he negotiated a new existence as world champion and member of the Nation of Islam, changing his name from Cassius Clay to (initially) Cassius X in a key transitional moment. It is written by Scottish author and producer Stuart Cosgrove, adapting his own 2020 book Cassius X: A Legend in the Making.

This perfectly watchable film moves with breezy fluency from Ali’s early years, the sensational gold medal at the 1960 Rome Olympics, the hilarious star-is-born interviews and media proclamations, the creepy cabal of white Kentucky businessmen who banded together to promote and manage Clay (as he then was) as they would a racehorse – and ending up with his sensational victory over Sonny Liston in 1964 (which is shown at almost real-time length) and Clay’s announcement of his conversion to Islam. As in Leon Gast’s 1996 film When We Were Kings, archive material is interspersed with interviews with grizzled old sportswriters, one of whom tells us about his own background at questionably interesting length. We also get interesting encounters with Ali’s ex-fiancee Dee Dee Sharp and Malcolm X’s daughter Attallah Shabazz.

There is a lot to enjoy here: particularly his hubristic encounter with Britain’s Henry Cooper in London whom Clay mocked in the ring by dropping his guard; Cooper punished this by actually knocking him down. If this hadn’t happened just before the end of a round, and if trainer Angelo Dundee hadn’t cunningly bought more time by claiming his man had a ripped glove, he might well actually have been defeated. (As it was, Henry Cooper could claim the Jake-LaMotta-ish distinction of not having been knocked out, the fight stopped because of his cut. It is a measure of Cooper’s quaint underdog status that the fact of Ali’s near defeat at the hands of a white man hardly figures, then or now.)

But what about Ali’s painful split from Malcolm X? It was Elijah Muhammad who gave Ali his new name, the Nation of Islam leader who rebuked and rejected Malcolm X, a key figure in Ali’s religious awakening, for his insubordinate attitude; and Ali unhesitatingly sided against Malcolm. This vital subject is really not discussed at any length at all and it is a flaw in this documentary – but no film can go wrong with a leading man of such star quality.

• Cassius X: Becoming Ali is released on 13 October in UK cinemas.