Richard II, Henry IV, Part IHenry IV, Part II, Henry V, The Roundhouse, London

"Over my dead body", is no mere figure of speech where Richard II and his successors are concerned. In Michael Boyd's powerful tetralogy (Richard Twyman is his associate for three of the plays; he directs Henry IV Part II), King Richard steps to his throne atop the corpse of the murdered Duke of Gloucester and is, in turn, cut down by an ally of the usurping Henry Bolingbroke. But Richard does not lie still in his coffin. He stalks, in his bloody shroud, through Henry IV, observing the constant rebellion and slaughter of the new king's reign. When Henry's son defeats the French, they meet atop a sea of coffins that hold the dead of Agincourt.

The Roundhouse comfortably accommodates Tom Piper's Stratford set – a copper-coloured engine-room of the monarchy that forms a sober backdrop to Piper's and Emma Williams's costumes, which, lovely in themselves, strongly characterise the actors inside them.

Richard's courtiers, in dark velvet, fur, and brocade, convey the softness and luxury of the king's self-absorption while setting off his own dress – a robe of white and gold that is a near-copy of the gown worn by his queen. In a mop of red Shirley Temple ringlets, Jonathan Slinger's Richard, prancing, pouting and delivering silky insults like Cecil Beaton at a Mayfair cocktail party, comes too close at times to mere vulgarity. But the aggressive frivolity, as well as making Richard more than usually responsible for his overthrow, provides a painful contrast to the grief – not only for himself but for his country – that turns this puppet into a king only when stripped of his crown. No longer preening himself on his importance, he attains humility and tragic grandeur on realising what a little thing he is in the face of God and history.

Clive Wood's robust, businesslike Bolingbroke, dressed, like his counsellors, in narrow-fitting, puritanical black, has no need to change when he assumes the throne. But his son, Geoffrey Streatfeild's restless Prince Hal, realises all too well that the crown that awaits him will demand a wise head. When, carousing with Falstaff, he imitates his censorious father, Hal lashes his own folly in a manner that suggests ridicule less than a displaced confession of guilt.

Leaving his coronation, the new Henry V awkwardly tells his beloved friend, "I know thee not, old man" as if sickened by the words he forces himself to utter. Well before this, however, David Warner's touching, semi-detached Falstaff sees the sorrow ahead for both men and even hints that the king, in abnegating self to duty, has taken the cue from the aged knight's obliteration of self in a dream of pleasure.

In all these plays, the verse-speaking is of a high order – always clear, fluent, and natural, occasionally of a startling freshness. Richard's death assumes a sickening physical reality when his last words are delivered in a rush, as if he suddenly realises he might not live to the end of the sentence.

Lex Shrapnel's graceful Hotspur, instead of maintaining his rage at his father to the end of his speech, ends a series of angry rhetorical questions with a thin, mocking, "No?". Vocally and physically, the actors enliven the Henry plays with plenty of humour – Geoffrey Freshwater's awful-but-irresistible Justice Shallow is a particular delight, and the cheeky anachronisms (including one roisterer's fleeting suggestion of Russell Brand) and the departures from the text are too few and too amusing to be objectionable.

For all the company's skill and style, however, the plays lack five-star sex appeal – there is no actor with the magnetism and danger to lift this series from deeply satisfying to overpowering. That said, I was very taken by Miles Richardson, who, as the Duke of Exeter and in two smaller roles, suggests a sinister figure more at home in The Duchess of Malfi but assumes, as he prepares to attack the French, a thrilling expression of blood-curdling savagery. But maybe that's just me.

To 24 May (0844 482 8008; www.thehistories.co.uk)

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