The Cuckoo Club is a swish, luxuriously upholstered private members bar and restaurant, just off Regent Street, where everything that isn’t leather, velvet, silk or glass is gleaming stainless steel, or something that looks like it.

This early Monday evening, it’s packed – ostensibly for a showcase performance by the Honolulu-born singer and pianist, Anjani, here to promote her new Sony album, Blue Alert.

What most of us are here for, if we’re honest, is, however, a glimpse of Anjani’s what I suppose you’d call ‘mentor’ – Leonard Cohen, who co-wrote and produced the album.

More cynical souls than myself doubted he’d be here – but that’s him, at a small table about five feet from where I’m sitting, sipping a glass of beer and mouthing the words as Anjani essays a supremely tasteful version of “Blue Alert” and almost audibly purring with approval for what she’s doing.

Cohen had made a brief speech earlier, to introduce the singer and her backing trio – handpicked jazz veterans, as perfectly groomed as their surroundings. As was Cohen, of course, a handsome 73 now, with close cropped silver hair and a slight stoop, but wholly elegant, like some Democratic elder from the American heartland, a senator or congressman with an impeccable record on all the important liberal issues. There is much mischief about him, too, an eternal liveliness that age has evidently not impaired.

“This ritual is very new to me,” he says dryly of the showcase. “I enquired of someone what the audience would be like. ‘Indistry people,’ he said. I immediately thought of the cast of Night Of The Living Dead, shuffling towards the stage with something on their minds other than an appreciation of music.”

Anjani, nervous but composed, plays a selection of well-received songs from the new album, thanks Leonard effusively at every opportunity, and is clearly heartfelt in her appreciation, Anjani dreamy-eyed as she gazes swoonsomely at Cohen when he joins her for a touching duet on “Never Got To Love You”, and later on something very tender called “Whither Thou Goest”, after which they go, Cohen giving a little Zen bow to the boys in the band before making an impeccably dignified exit.

An entirely unexpected start to the week, then.