It sounds irresistible, doesn’t it? A National Theatre Live version of a play by Jack Thorne (the magician who conjured up Harry Potter and the Cursed Child and that re-animation of A Christmas Carol) about the 1964 Broadway production of Hamlet starring Richard Burton with Sir John Gielgud directing. The Motive and the Cue has Johnny Flynn in a brown wig discernibly imitating the lustrous Burton voice with its Welsh underlay and its burnished metallic precision and Mark Gatiss as the languid old eagle, balding and forever bitching, who was more or less universally accepted – by everyone who didn’t have an allergy to his mellifluousness – as the greatest Hamlet of the first half of the twentieth century. At his finest perhaps in his twenties because he didn’t look, as he later did, as if he had God on his side.

Burton had played the Prince to Claire Bloom’s Ophelia in 1953 and found himself echoed from the stalls – no matter how much he went slow or fast to throw him off – by a booming Winston Churchill. The man who had delivered ‘We shall fight on the beaches’ – and originally written it in blank verse – appeared in the 28-year-old Welsh boy’s dressing room and said, ‘My Lord Hamlet, may I use your bathroom?’ A few years later when he was asked who he wanted to recite his speeches for the documentary The Valiant Years with music by Richard Rodgers he replied, ‘That fellow from the Old Vic.’ Why belabour the background to a weirdly conceived stage show? Because The Motive and the Cue is a fascinating prospect for anyone interested in Shakespearean theatre. Burton was King Arthur in Camelot to Julie Andrews’ Queen Guinevere in the production that haunted John F. Kennedy and then he did Cleopatra with Elizabeth Taylor. His Leamas in le Carré’s The Spy Who Came in from the Cold is an enriching characterisation – better than the figure in the book – and not long after the Hamlet there’s his George to Taylor’s Martha in Mike Nichols’ film of Edward Albee’s Who’s Afraid of Virginia Woolf every inch the equal of Brando in Streetcar.

Mind you Gielgud’s Cassius in Joseph Mankiewicz’s Julius Caesar – with Brando’s Antony and James Mason’s Brutus – is incomparable.

So what are the ghosts of these titans of acting doing in this celebrity story posing as a piece of drama? On a good day – say in Martin McDonagh’s Hangmen – Johnny Flynn is a superb actor with that insouciant and insolent boyishness which would have made him an ideal interpreter of Joe Orton’s Entertaining Mr Sloane. Hopping about in his jocks and vest mouthing drunken garrulous and sentimental slush he looks with his brown wig and his palpably approximate somersault towards the great voice of the actor who is said to have been one of the finest of all Iago’s – with a cutting edge plausibility – like a schoolboy caught in the acrobatics of a bad dream. A bit surprisingly, the far from easy on the eyes Mark Gatiss is distinctly superior as Gielgud if only because he retains a touch of humanity. Admittedly, if this were ever to be fully filmed it would be preferable if Gielgud were played by someone with a parallel but distinctive actorly magnetism – Ralph Fiennes, say, or Jeremy Irons – so that there would actually be a dialogue of styles with a distinctive edge. But Gatiss does pretty well under the dramatic circumstances.

Audiences will be boggled to discover – perhaps they will be pleasantly surprised – that vast chunks of The Motive and the Cue are given over to bits of Hamlet. This kicks things on even if it looks shameless. There is an extended bit of Johnny Flynn doing ‘O what a rogue and peasant slave am I’ with a bravura and bombast that is captivating in an over the top way. Then again Sarah Woodward as the Queen (played by Eileen Herlie in the original production) does a rather beautifully inflected version of the Willow speech.

Gielgud’s original conception involved nineteenth-century actors in rehearsal clothes but this tends to go by the wayside in this Sam Mendes production. And what a strange thing it is to have a noted film director allowing this play to go before the public with such big acting.

There are scenes of Burton abusing Gielgud with alcoholic lunacy and then there are scenes of abject grovelling. Burton who was the juvenile lead in Christopher Fry’s The Lady’s Not for Burning with John Gielgud revered his mastery of verse.

Nevermind Tynan saying scathingly that Sir John was the greatest actor in the world from the neck up: the man who was better at performing Under Milk Wood than Dylan Thomas thought Gielgud knew everything about the music of poetry.

It’s neat that Hume Cronyn – probably the greatest Polonius who ever lived – is highlighted among the actors: it allows for a practical demonstration of Hamlet running him through. There is also a very serviceable book Letters from an Actor by William Redfield who played Guildenstern in the production which might have been more profitably used and there are plenty of people still alive who saw the show.

It’s also odd to have so much needless inaccuracy. It was James Agate (the reigning critic of his day) who said Olivier’s 1930’s Hamlet was the finest performance of Hotspur he had ever seen. And Gielgud’s professed desire to do an underpants ad (‘at my age there’s not much action on the Y front’) makes more sense at the advanced age he actually said it.

But nothing that can be said against The Motive and the Cue is going to stop people flocking to it for understandable reasons. It’s in select cinemas from 5 April.

The Australian Ballet is leaving the State Theatre for the next couple of years but its closing production there is a wonderful Alice’s Adventures in Wonderland which on opening night was marvellous. It was led by Benedicte Bemet in a cast with no weak links.

In the short decade we’ve had it this Alice has shown it is a tremendous quasi-psychedelic take on the greatest of Victorian fairy tales but what a fabulous piece of ballet accommodated with such scenic metamorphosis from the lighting design by Natasha Katz, the sets of Bob Crowley, and an already classic score by Joby Talbot which makes you proud of contemporary composition.