Christopher Logue (b1926) has been working on his acclaimed mosaic of versions from Homer’s Iliad since 1959, when he began with a commission from BBC radio. This fifth and penultimate extract, Cold Calls, deals with the crisis faced by the Greek army when its champion Achilles angrily withdraws from combat after Agamemnon, the commander-in-chief, steals the slave girl Briseis from him. It closes with Achilles’ s ultimatum to the desperate Greek envoys. Unless he receives satisfaction he will sail home and leave them to the currently rampant Trojans.

Logue is not a classicist and began without knowing Greek. Of the work as a whole, he has commented that he hoped he was writing “a poem in English” rather than attempting a faithful reproduction of the original, and in support has cited Samuel Johnson’s belief that “We must try its effect as an English poem . . . that is the way to judge of the merit of a translation.” There are those who might disagree with the broad permission thus granted. Logue cuts, reorganises and is at times cheerfully anachronistic: the goddess Aphrodite, for example, mother of the Trojan prince Aeneas, is called here “Our Lady of the thong”, while the gods in general behave like a ghastly family of celebrities — and are the least interesting feature of the book. But if we side with Johnson it is clear that what Logue writes has a compelling life of its own, particularly in its unmediated savagery. It is difficult to convey the horror of violence afresh, but Logue appears to understand the unapologetic, craftsmanly attitude of a warrior society. Here Aeneas beheads an opponent: “Took his head off his spine with a backhand slice — / Beautiful stuff . . . straight from the blade . . . / Still, as it was a special head, / Mowgag, Aeneas’ minder — / right as a box of rocks, but musical — / Spiked it, then hoisted it . . . twizzling the pole / Beneath the blue, the miles of empty air”.

That gleeful celebration of atro-city speaks to our own age, from Stalingrad to Chechnya and Iraq. Both Quentin Tarantino and bad British gangster films attempt an equivalent swagger, only to end up with a pose. In this Iliad, however, there is no escape into alleged irony. Nobody leaves before the end, and there is nowhere else to be but on the plain before Troy.

It must be tempting to produce a richly decorative version of The Iliad, full of local flourishes and curlicues. In Cold Calls, Logue’s economy is severe: nothing is present solely on its own account; everything serves the complete, chilling effect. His work has been called cinematic, and in an austere, functional sense this is true, as in the chariot-borne spear-duel between Hector and Diomedes: “Those skewers trading brilliance as they passed — / And missed — both vehicles slither-straightening”.

The poem comes back over and over again to the blood-soaked killing ground between Troy and the sea, dramatising the double time-scale: on the one hand the daily grind and uproar of fresh battle, on the other the slipping-away of 10 years in virtual stalemate. War becomes a machine for reproducing itself, while the Greek commanders squabble on their hill of bones. In Achilles’s response to the pleas for him to return to battle, Logue imports a Tennysonian note in such a way as to upend it, to complex effect: “My mother says I have a choice: / Live as a happy backwoods king for aye; / Or give the world an everlasting murmur of my name, / And die. / Be up tomorrow sharp / To see me sacrifice to Lord Poseidon and set sail.”

Achilles must serve as his own mourner. Colonel Tim Collins would understand this blend of the sentimental and the authentic, as well as knowing its effect on the like-minded.

There is nothing in Cold Calls that quite rivals Logue’s amazing rendering of Achilles’s fight with the river Scamander in Book XXI, whose lavishness makes plain that his methods elsewhere are the result of choice rather than limitation. But this is hardly Logue’s fault. The question now is how long we must wait for the appearance of the whole of his version in a single edition.