Every gig at the Royal Albert Hall feels special, that’s a given, but Nine Inch Nails were clearly intent on going one further when they announced their one-off gig at the hallowed London venue. Arranged in front of a canvas backdrop upon which the sinister shadows spin and distort, these titans of industrial rock play one of the RAH’s most thrilling shows in recent memory.

NIN have never really been one of those bands who insist on sticking to new material after a recent release (they just dropped their ninth studio album Bad Witch) and frontman Trent Reznor goes so far as to joke about how most of the tracks on their latest offering are “f**king fast”; a slightly strange almost-apology. Bad Witch is easily the shortest work to pass for a NIN album, but is also one of their most subversive, punctuated by abrupt breakbeats and an apparently new energy from its 53-year-old frontman.

The band delve as far into NIN's back catalogue as “Wish” from 1992 EP Broken: the show opens with a maelstrom of lights and drumming prodigy Ilan Rubin going hell for leather; driving the track’s thundering, intricate rhythms with a sophistication and zeal that mirrors Reznor’s own sublime performance.

A rendition of the lingering “Frail” from 99’s acclaimed, multi-textured record The Fragile is poignant and has most audience members holding their breath – apart from one cretin who decides to bellow “hurry up” for one or two cheap laughs and thousands of other irritated murmurs – but Treznor ignores him. The song cuts abruptly, as many in this set do, and the lights drop, plunging the venue into darkness.

“S**t Mirror” off Bad Witch makes its live debut; an acid-soaked rave track which reprises much of the aggressive power heard on their first two EP releases: there are punk guitar riffs and Reznor’s squalling, distorted vocals drift up to haunt the highest reaches of the venue: “I’m becoming something new/It’s getting hard to recognise.”

Meanwhile “God Break Down The Door” and “Copy Of A” are sandwiched around a version of the instrumental track “Parasite” - lifted from Reznor’s side project with bandmates Atticus Ross, Rob Sheridan and Reznor’s wife: the singer Mariqueen Maandig. There’s also a superb, endearingly joyful version of Joy Division’s “Digital” with multi-instrumentalist Alessandro Cortini doing justice to the track with a slightly squelchier take on that thrumming bass line.

14 songs in and Reznor announces the last performance of a Bowie cover, of “I Can't Give Everything Away” from the late artist's final album Blackstar. It's impossible to quantify just quite how much of an influence he had on Reznor - personal and artistic - Bad Witch is practically haunted by his ghost (the mournful sax heard on songs such as "God Break Down The Door" was directly influenced by Blackstar), and Reznor has spoken plenty of times in the past about how he obsessed over the clues Bowie left in his music. “He was a tremendous inspiration in terms of what was possible, what the role of an entertainer could be, that there are no rules," he wrote in a moving Rolling Stone tribute.

As they round off the night with an encore that features a breathless performance of Year Zero’s “Survivalism” the crowd reaches fever-pitch; fans in the standing area (as if everyone in the venue hasn’t been standing since the first track) hurl themselves into one another as a moshpit near the front widens; one fan crowdsurfs momentarily before toppling over the barrier.