Was Rufus Wainwright made for the Proms? Quite possibly: he ticks all the boxes needed for the ideal late-night set. He’s a pop artist, yes, but a pop artist whose love of classical music (Romantic opera especially) informs almost everything about him, from his vibrato-heavy voice to his occasional quoting of Ravel’s Boléro. It’s an ideal match between the Proms’ generally classical-first ethos and the more laid-back atmosphere the late concerts foster. And this was also a showcase for the always impressive Britten Sinfonia, acting as a backing band in this set of mostly new orchestral arrangements, as well as rising-star conductor Johannes Debus. Also: Deborah Voigt popped in for a couple of numbers. What could possibly go wrong?

Well, a few things did, but overall Wainwright’s charm and the quality of his pop songs won out. After the dust had settled on his touching encore, however – Over the Rainbow, of course, with a digitised rainbow popping up on the LCD board behind the stage – it felt like the concert had missed a lot of opportunities.

Wainwright was at his best in the second of his two sets, which were separated by Voigt’s cameo: in this set, unlike in the first, he sat at the piano and accompanied himself and the orchestra, and the whole thing came together in a way it hadn’t earlier on. Going to a Town, I Don’t Know What It Is and Cigarettes and Chocolate Milk were a superb trio of big songs well played, and I Don’t Know What It Is was the most interesting of the new arrangements, a real recomposition for this orchestra which discarded a rhythm section for most of the song. Poses was also well performed, but there was no need to smother the song, his best by miles, with this fancy arrangement when its soul resides in the gently rocking piano chords and Wainwright’s huge, crooning voice.

A lot of the first set, too, was awkwardly or unnecessarily arranged, and the balance between voice and orchestra was frequently way off – putting mics everywhere might plausibly have been a necessity, but having the orchestra so high as to drown Wainwright out was surely not. They weren’t always fully together, either, although the sweet, xylophone-rich version of Tiergarten and the rapid string playing in Who Are You New York testified to the talent of all involved. What a shame, though, that The Art Teacher – originally a tender, affecting ballad with Wainwright accompanying himself on piano – was muffled under a gloopy layer of strings. Sadly, this was typical: most of the arrangements (predominantly by Maxim Moston) were more or less proficient, but didn’t embrace the potential offered by having a virtuosic band like Britten Sinfonia to play with, and never really justified themselves.

Another missed opportunity was not doing more with Deborah Voigt, one of the world’s great sopranos, who was making her first Proms appearance since 2007. She sang two extracts from Wainwright’s debut opera Prima Donna, but even her marvellous voice could not make something of material which, throwing the baby out with the bathwater, contains little of the charm or wit that mark Wainwright’s pop music out. Voigt got more of a chance to shine in a duet – “If I Love You” from Carousel – but after a stellar first verse from her, Wainwright forgot the words and then oversang into his microphone.

It didn’t really matter, though, because Rufus Wainwright oozes charm and talent and is remarkably good at remaining likeable, even when forgetting his words or name-dropping horribly (at one point he thanked Helena Bonham Carter’s mum for a brooch he was wearing). Packed to the rafters, the Royal Albert Hall was eating out of his hand. This was such a natural fit for the Proms, it didn’t even feel like a debut. I’m sure he’ll be back. If he can push the envelope a little more next time, so much the better.