The practice of commissioning new ‘cover versions’ of venerable, canonical texts is odder than it might at first seem. It’s hard not to see it as a back-handed compliment, even a bit of a telling-off. Good old Aeschylus may have meant well, but here’s a few things he didn’t understand. In the case of the Hogarth Shakespeare series, what is retained from the source text – character and plot, in various degrees – might anyway be viewed as less congenial to the intelligent modern reader than what is by definition lost: namely, the deep structures and resonances on the one hand and the beautiful, burnished language on the other.

Nevertheless, the list of authors so far assembled for the task shows a certain shrewdness. Jo Nesbø, the doyen of Scandi noir, is tackling Macbeth: you can almost picture the woods on the march, in bleak high-contrast monochrome, while the thanes scratch their beards existentially. Howard Jacobson, a rhapsode of middle-aged male apoplexy who is also a great moralist and a forensic observer of Anglo-Jewish attitudes, has transplanted The Merchant of Venice to Footballers’ Wives territory. And here Edward St Aubyn, whose Melrose novels explore a particular nexus of unkindness, sadness, poshness and wit, gives us his take on the mother of all dysfunctional-family sagas, King Lear.

St Aubyn’s Lear is Henry Dunbar, a bearish media mogul. We encounter him not preparing to divide up his kingdom but in medias res, cloistered in an expensive sanatorium, as if there is any other kind, in the Lake District after his two ‘bad’ daughters, Megan and Abby, with the help of their lover and sidekick Dr Bob, have engineered a mental health crisis that left him gibbering on Hampstead Heath. As Dunbar begins, Henry is refusing medication and plotting his escape, aided and abetted by Peter Walker, a celebrated television personality and committed alcoholic.

A clock of sorts is ticking: the bad sisters have some skulduggery planned for an upcoming board meeting, while the ‘good’ one, Florence, is on her father’s trail, with a little help from Wilson, formerly Dunbar’s consigliere – recently cast out of favour, like Florence, for no particularly good reason – and his son, who is also Florence’s once and (who knows?) future squeeze. Meanwhile Dr Bob, whose devotion to Megan and Abby is perhaps understandably tested by having one of his nipples bitten off during a pill-fuelled threesome, has his own agenda to pursue.

Sorry, that’s quite a lot of exposition. It’s true that the narrative element of Dunbar, while lacking the convolutions, doublings and (let’s face it) longueurs of Lear, is much more eventful than admirers of St Aubyn’s Melrose novels may have learned to expect. The entire plot of Bad News, more or less, is: ‘Will Patrick get his hands on some drugs at some point?’ Gripping enough, in its way, but only because of the company we keep while we’re waiting to find out. Maybe this was part of Lear’s appeal for St Aubyn: a chance to flex a different set of muscles; the middle section of Dunbar is as skilfully paced as any thriller. But it doesn’t give the other stuff, the arrangement noted above, as much room to breathe as in the past.

It doesn’t help that while this lot are rich and powerful, they’re not exactly posh in that ancient, threadbare way we see in the Melrose books – they’ve never known bad plumbing or had to eat lukewarm grouse. There’s never that sense of the precariousness of money: even when cut off by her father, Florence still gets to hang on to the satellite trust fund and the farm in Wyoming. Consequently – and ironically, given the project at hand – a certain tragic register is missing, though Dunbar rages and sobs competently enough.

St Aubyn’s eye for specifics is as keen as ever. Dunbar has Chardins and William Nicholsons in his private jet; there’s a hilarious digital tycoon, jabbering away on the phone, surrounded by TV screens, pinioned to his exercise bike like a mad centaur. He also sketches characters confidently and economically, from Simon, the tramp Dunbar encounters while on the lam, to Abby’s conscience-stricken husband, the crushingly spondaic Mark Rush. There is even a certain amount of wit. But you don’t quite get the sense that the wit stems from and feeds off the unkindness and unhappiness, as you do with Patrick’s clan.

If Dunbar doesn’t quite feel like a free-born St Aubyn novel, how does it serve its source text? Pretty well, overall, not least because it doesn’t strive to cleave to it too closely: there’s a Fool, three sisters, various intriguing courtiers, an Albany, and a Kent in the form of Wilson, but you’re never reduced to ticking off entries in your concordance. There’s no vile jelly, either, though Dr Bob’s pharmacological mischief and an incident with a can of petrol ensure a certain level of Grand Guignol is maintained. Of course, King Lear is itself a cover version – one, furthermore, that’s since been stress-tested in the theatre for three centuries. If it can survive Brian Blessed, it can survive anything.

The most interesting thing about Dunbar in a way is its treatment of the three sisters. King Lear is, fascinatingly, a play with no mothers in it, though Lear tries to fill the vacancy with each of his girls in turn. It’s his insistence on professions of unconditional, maternal love – professions that Regan and Goneril are only too happy to make – that makes everything go to pot in the first place, of course. We don’t get to see Dunbar make those demands, though his monstrous narcissism is never in doubt. But we do find out, plausibly enough, that he has always favoured Florence over her half-sisters because her mother Catherine was the love of his life. During his brief idyll of reconciliation with Florence, he even calls her ‘Catherine’ – though that could be the drugs.

Megan and Abby, meanwhile, are presented as archetypal motherless children: packed off to boarding school, they torture a classmate who’s had an abortion by furnishing her room with baby kit and cuddly toys (‘they had literally emptied the Slough branch of Mothercare’). This part is done with a certain brisk humour (it’s also one of the few parts of the book where we see the real corruption behind the Dunbars’ power, as the sisters bully their way out of trouble with threats of a media monstering). But some readers may bristle at the suggestion that their depraved natures are somehow of a piece with their divergence from traditional womanly expectations, be it their contempt for motherhood or their fondness for athletic, affectless, sado-masochistic sex.