The dynamics of the rock group. A riddle, wrapped in a mystery, inside a tour-album-tour schedule.

Getting Things Done, even in rock’n’roll, tends to require a leader. Said leader is normally the frontman or the principle songwriter. When those responsibilities are split (Jagger-Richards, Lennon-McCartney, Page-Plant, or Bruce Foxton and Rick Buckler asking for more responsibility), problems ensue.

This, in part, what makes the documentary New World Towers about the making of Blur’s last album The Magic Whip, so engrossing.

To recap: Damon Albarn is as much of a de facto benevolent dictator as you can get in modern music. He’s the creative fulcrum for all of Blur’s songs and the band’s frontman, as well as being the co-creator of a Chinese opera, a National Theatre musical based on Alice In Wonderland, two bands with Paul Simonon from The Clash and Flea from the Red Hot Chili Peppers, plus four, soon to be five, albums from cartoon band Gorillaz.

Albarn may have shared the publishing with his three art school-era friends (guitarist Graham Coxon, bassist Alex James and drummer Dave Rowntree) but rarely the critical acclaim. He has, until now, been credited with keeping the show on the road.

It was seriously derailed at the end of the century, which was certainly nothing special for its guitarist. His erratic behaviour led to Blur’s manager asking him not to come to the recording of 2003’s Think Tank after he had contributed only one track. A reconciliation between Coxon and Albarn followed with Hyde Park gigs in 2009 and 2012, but the last album Blur made as a quartet, 13, predated the Millennium.

The documentary New World Towers, screened this week on Sky Arts, tells the story of Coxon usurping Albarn as the band’s leader, however momentarily.

As follows the Acts I-III structure of so many films, Act I sees things going well – the four reunited on tour in Hong Kong with time to kill when a gig in Taipei falls through. They head to the studio. We see footage of one of England’s biggest groups travelling together on the tube, and Coxon junking one song because it sounds too much like Whatever by one-time rivals Oasis. 20 songs are recorded. Towards the end of recording (Act II, if you like) Coxon seems to lose faith in the project.

As Albarn tells the documentary makers: “He had a bit of a wobble at the end of the five days and I thought ‘here we go…’ ”

This is when the story changes direction. Coxon, at one point by common consent the most unreliable member of Blur, quietly takes the recordings months after they have been apparently abandoned and goes to Stephen Street, the producer of Blur’s albums from Modern Life Is Rubbish to 1997’s Blur album.

Street and Coxon work on what becomes The Magic Whip and take it to the man who’s normally expected to Get Things Done for his approval. Albarn is in reassuringly Man from Del Monte mode and The Magic Whip was released in April 2015 with next to no pre-release hype. It stands in comparison to many of the band’s most successful albums. The standout track, the ballad My Terracotta Heart, touches on the singer and guitarist’s often fractured relationship and in the film we see it performed.

During the song, Albarn stares behind the keyboard longingly at his best mate, singing “When we were more like brothers” before musing aloud “If I’m losing you again.” Through this, Coxon doesn’t take his eyes off his guitar.

When Albarn tells the 2015 audience at Hyde Park “thanks to Graham for the album,” it feels like the balance of power in the band has quietly shifted a little. Not that Coxon’s eyes would leave his guitar long enough to well up.

Coxon likens himself to a “mardy-arsed teenager” in the film but in some respects he’s as important to Blur’s success as the singer. Most of their greatest songs – Beetlebum, Song 2, Tender, This Is A Low, Chemical World – are impossible to imagine without his contribution. In between Blur, he’s managed to record eight solo albums (to Damon Albarn’s paltry one) and played gigs with Paul Weller, Robert Plant and Noel Gallagher. In 2016, he also helped organise a tribute concert to his hero Bert Jansch and give an Ivor Novello lifetime achievement award to Albarn.

It’s Blur’s guitarist who may be due some recognition of his own. Coxon’s formative years as a saxophonist (he still plays) informs the idiosyncratic way he plays scales on his Fender Telecaster. Born in Lower Saxony, Coxon’s father Bob was stationed as a clarinetist player for the British Army. Coxon Sr. was also the band leader.

The apple perhaps fell less far from the tree than we could have first imagined.