The setup: Tim Minchin is clever. That word is almost an insult in the performing arts, implying a kind of shallow ingenuity too satisfied with its own accomplishment. And yes, Minchin – the privately educated son of a surgeon – is sometimes that. But in musical comedy, his niche, he needs to be. Funny songs are hard, but Minchin succeeds because he is relentlessly inventive.

After coming to prominence in 2005, his rise was fast, and this show – more than two hours long, performed with a full orchestra in the Albert Hall – marks a climax about as high as any comedian can go. Knowing this (and Minchin is always knowing), he begins with a parody of an overblown beginning, writhing in a smoke-filled cage singing, "I'm in a cage!"

Soon he is swimming through a prog-rock epic about "a nerd" too straight, and now too old, to realise his dreams of being a rockstar. "He knows his music lacks depth, but it can't be helped/ He has nothing interesting to say, so he writes about himself./ But he doesn't want to seem self-obsessed, so he writes in third person." Strum these out unplugged and they'd be merely witty, but with all the grandeur that Minchin musters for a line like "But I'm famous now, so suck my balls" he really is quite something, like a mock-rock Salieri.

Funny, how? Minchin is always keen to stress that he is only a "hack pianist", although he surely knows that in variety and ambition he is far ahead of distinguished predecessors like Tom Lehrer, Victoria Wood or Victor Borge. Stranded where he is, however, on the middle of a sagging tightrope between the heights of comedy and music, he clearly feels impelled pull a lot of stunts. His use of the orchestra not only to deepen his music, but to score his jokes and punctuate his commentary, is brilliant. The unfinished song Con, about his prejudices, which turns out to be called Context when it's resung with the missing lines, is about as ingenious as song-writing gets. Except perhaps for this three-minute number he wrote about writing a three-minute number.

That's the other thing about Minchin. Some people (and some famously) don't care for all the makeup and find him smug, but there can be few comics who put more work into their performances. (And there would be none who'd take home less money after a show of this size – that orchestra must have cost a fortune.)

Nor are there many artists of any kind who have sustained a focus in their work like Minchin's stand against religion. His Dawkinsian assaults on the Pope, the Qur'an, miracles and superstition generally are as funny as they are acute, and they have brought him a large following of the like-minded. Don't expect the same steadiness in the stream of laughs that standup comedy delivers, but you will laugh – plenty – and, from time to time, you'll look down and see your foot is tapping too.

Comic cousins: Bill Bailey, Victor Borge, Victoria Wood, Tom Lehrer, Flight of the Conchords, Robin Ince, Eddie Izzard

Steal this: "There's only one thing in this world that I hate more than racists. Filipinos."