Michael Coveney: Benedict Cumberbatch helps put his relative Richard to rest

King Richard III, aka Laurence Olivier in the great movie, Antony Sher on crutches as a gleaming, spidery hedgehog for the RSC, and soon-to-be-on-BBC-TV Benedict Cumberbatch, is re-interred today at Leicester Cathedral in a ceremony led by the Archbishop of Canterbury. The medieval monarch, whom members of the Richard III Society claim was outrageously slandered in Shakespeare's play, died at the Battle of Bosworth in 1485.

Obviously our greatest dramatist misheard his dying cry of "A hearse, a hearse, my kingdom for a hearse." His corpse has suffered many indignities since his first burial, and was allegedly thrown into the River Soar after the dissolution of the monasteries before being discovered in a car park in Leicester three years ago; thousands of people have filed past his casket in the cathedral this week.

Top of the bill today – well, just behind the Archbishop – will be Cumberbatch himself, reading a poem; it transpires that Bendy is very distantly related (second cousin, 16 times removed) to the child murderer, though he's not, as far as I know, claiming any family resemblance. Maybe he'll feel more murderous after all the Hamlet hoopla at the Barbican in August. Meanwhile, the city of Leicester is cashing in big time on the re-burial, spreading the event across five days with a huge influx of tourists and foreign visitors and all the trimmings – T-shirts, rose-flavoured ice-cream (Richard was a Plantagenet king defeated in the Wars of the Roses), fridge magnets, haircuts and silk ties. There's even, let's make no bones about it, a pop-up visitors' centre next to the car park.

Thanks to Shakespeare, we think of Richard III as a "wicked" king, one of the few; another was King John, though he's more politically pathetic than violently obnoxious in Shakespeare's lesser known but very interesting play about him, soon to be revived by director James Dacre for the Theatre Royal, Northampton, as part of the 800th anniversary of Magna Carta, with performances at the Temple Church in London in early April. "King John," wrote Winnie-the-Pooh author A A Milne, "was not a good man, he had his little ways, and sometimes no-one spoke to him for days and days and days. And men who came across him, when walking in the town, gave him a supercilious stare, or passed with noses in the air, and bad King John stood dumbly there, blushing beneath his crown."

Would Richard III have blushed beneath his crown? I doubt it, and he would probably have preferred to be remembered for his stage reincarnation by such great actors as Olivier and Sher, not to mention the greatest I ever saw in the role on stage, the Georgian actor Ramaz Chkikvadzye, as well as the French star Robert Hirsch and our own Ian Holm and Ian McKellen. The McKellen performance is preserved on film in a heavily cut version by Richard Loncraine based on Richard Eyre's National Theatre production, and it's a hoot, the chain-smoking 1930s fascist consumed in an inferno at Battersea Power Station to the ironic accompaniment of Al Bowlly singing "I'm sitting on top of the world."

The real Richard III only reigned for two years and is credited with various trade and financial reforms for the better. Although contemporary portraits suggest he had one shoulder higher than the other, there is no evidence that he was a hunchback; so it's hilarious that the apologists for the validity of the Leicester remains have made so much of the bones showing evidence of curvature of the spine, which only corroborates Shakespeare's myth, not historical truth.

Wanamaker stuns as Stevie

A couple of other West End corpses are currently on show at the Haymarket and Hampstead. Mary Chase's Harvey and Hugh Whitemore's Stevie – about, respectively, a dipsomaniac eccentric with an invisible white rabbit and a suburban poet with a maiden aunt – were seen within two years of each other in London in the mid-1970s, and Mona Washbourne, a wonderful old character actress, was in both.

Her roles are now taken by Maureen Lipman as Harvey's sister and Lynda Baron as Stevie's aunt, and they're both terrific. As a part-time theatrical necrophiliac I like both plays very much, but despite a rousing first night at the Haymarket and a packed out matinée yesterday at Hampstead, I can't see how modern audiences will find the time or patience to adjust to the altered cultural contexts for both plays.

Harvey, one of James Stewart's great film roles (and he played it, soporifically, on stage here in 1975) is a particular kind of American post-war eccentric in a world adjusting to the after-shock of conflict and the growth of the psychoanalysis business; while Stevie, first played by a 40 year-old Glenda Jackson exactly half-way through her stage and screen career, is a tender, experimental exercise in morbidity as popular poetry is annexed by the metropolitan intellectuals. Zoë Wanamaker gives a remarkable performance, and I loved, too, the clever contribution of Chris Larkin (Maggie Smith's elder son) as a narrator, fiancé and camp old literato shuffling his friend by car from Palmers Green to snobby salons and the BBC.

I'd forgotten the marvellous scene where Stevie Smith re-enacts her day at Buckingham Palace to receive the Queen's Medal for Poetry. Her vivid evocation of a vaguely disinterested monarch is surely the first imaginative representation of HMQ on the modern stage (in 1977), 12 years before a sly and dumpy Prunella Scales discussed the royal paintings with Antony Blunt in Alan Bennett's A Question of Attribution at the National. Now, of course, you can't move for royalty on the British stage – stand by for Kristin Scott Thomas in The Audience – and it's surely only a matter of time before someone comes up with an "authentic" version of Richard III in defiance of Shakespeare.