‘The last time I performed in London, I was shut in a box for 44 days.” And pelted with eggs, as David Blaine fails to add. That 2003 stunt backfired, but the stupefaction quotient is high in his touring show Real or Magic? which showcases Blaine’s magic as well as the lengths to which he can push his body. So too is the squirm quotient – I spent a fair chunk of the show looking at anything but the stage.

Squeamish viewers (that’s me!) will wonder how anyone could be entertained by the spectacle of a man piercing his biceps with a metal spike. Or, for that matter, vomiting up pints of water on demand to extinguish a fire. But even if the horror is sometimes a painful watch, the point it’s making – Blaine’s supernatural command of his body – is abundantly made.

At the interval, an amateur hypnotist beside me claimed you can trance yourself into not bleeding. That would certainly explain Blaine’s hangdog demeanour: if he’s in a trance, no wonder he’s not perky. I found that this kind of anti-showmanship makes the gruesome moments – stitching his lips together, say – feel even more confrontational. Then there’s the act two showstopper, when Blaine submerges himself in a water tank for 10 minutes without breathing. The drama requires cranking up, with live commentary, a countdown and some children loosed on stage to commune with Blaine through the glass.

The closing moments are the most human, as Blaine, recovering his puff, shares his belief that “we can always be amazed at the human body and what it does.” These feats of imperviousness and endurance risk overshadowing the actual magic tricks – inducing symbiosis in two unrelated audience members; guessing which jigsaw piece among 2,000 that his volunteer (Spider-Man star Tom Holland, as it happens) will choose. But each of them are astonishing, in their less showy way. No one throws eggs; there’s a clamorous standing ovation.

• At Eventim Apollo, London, on 19 June.