No literary artist, Martin Amis once wrote, ages more slowly than a poet, “some of whom (Yeats for instance) just keep on singing, and louder sing for every tatter in their mortal dress”. He could have been discussing the late-career flourishing of his old friend Clive James, who just keeps on singing even as his mortal dress is shredded by leukaemia, bouts of pneumonia and chronic emphysema.

We all live with the knowledge of mortality, with the sound of the clock ticking. But for five years now the clock has been threatening to stop ticking altogether for James: he has in effect been living under a death sentence that miraculously keeps being extended, like some death-row inmate whose lawyer keeps winning him a last-minute reprieve from the executioner’s needle.

James accepts that but for the expertise of doctors at Addenbrooke’s, his local hospital in Cambridge, and what he calls the “meds”, he would have been dead several years ago (he was first diagnosed with terminal leukaemia in early 2010). Several of the many autobiographical poems in Sentenced to Life, his latest and finest collection, express gratitude as well as bafflement that he is still with us.

When you are waiting to die, one course of action, James has said, is “inaction”. The other is “to go on working, as if you have all the time in the world”. For James work means reading and writing (he is no longer well enough to travel) — and these two books as well as several others that have been commissioned are testament to his remarkable resilience and industry.

The title of Latest Readings is self-explanatory: it is a collection of mini-essays about the books he has been reading and rereading. One encounters favourite writers such as Conrad, Kipling and Philip Larkin as well as those he previously neglected, such as Olivia Manning.

Like Orwell, James has infinite curiosity and seeks not to impose arbitrary distinctions between high and low culture — after all, he made his name as a brilliantly witty television critic for the Observer in the 1970s and as a reliably unreliable memoirist. He writes here that “culture is a matter not of credentials, but only of intensity, and sometimes you will find things out from fans and buffs that you won’t from a tenured professor”. This is well said, not least because in his own writing James combines a fan’s intensity with a professor’s erudition.

His qualities are his capacious intelligence, sardonic voice and fondness for wordplay and paradox. Hemingway, he writes in a reassessment of The Sun Also Rises, “overstated even the understatements”. Of VS Naipaul, he says we read him “for his fastidious scorn, not for his large heart”. And so he goes enjoyably on.

The style of these pieces is pared-down and reflective. Fragments of autobiography are scattered through them. He tells us how he came upon the books about which he is writing — some were already on his shelves at home but others were bought from the local Oxfam shop and a second-hand bookstall on Market Square, Cambridge, to which he shuffles when energy levels allow.

James writes here that ‘culture is a matter not of credentials, but only of intensity’. Although James is much better known for his work as a cultural critic and primetime broadcaster, he has been writing poetry since arriving from Australia to study at Pembroke College, Cambridge. It’s perhaps only in these last few years of terminal illness that he’s found his defining poetic subject, and for this celebrated humorist it turns out to be the gravest subject of all: death. Or, more precisely in James’s case, his principal subject is less death (which, as Wittgenstein wrote, is not an “event in life”) than the long, drawn-out process of his dying, which is very much an event in his own life.

Could it be that the imminence of death has liberated James into becoming the poet he longed to be? The urge to impress — you sense he always enjoyed being the smartest guy in the room — has been checked. Instead one discovers poems of formal restraint, humility (“Just for a time, so little means so much,” he writes in “Rounded with a Sleep”) and of a kind of baffled wonder at what JG Ballard, as he too was dying, called the miracle of life.

In “Driftwood Houses” he contrasts his plight (“I’ve hit the wall”) with memories of a long-ago family holiday when his daughters gathered shells on a beach and built houses roofed with towels. There’s a hint of regret but nothing mawkish or self-pitying in the poem, the final line of which suggests contentment: “As I lie restless yet most blessed of men.”

Restlessness has defined James’s life and work — restlessness with domesticity, with various literary forms, with finding the appropriate balance between pursuing a dual career as a TV entertainer and writer of serious literary ambition. If he feels blessed now, perhaps he didn’t always so, when he enjoyed what in “Landfall” he calls the “false freedom of excess”.

“The childish urge to understand everything doesn’t necessarily fade when the time approaches for you to do the most adult thing of all: vanish,” he writes in his introduction to Latest Readings. James has felt the pressure all too well of this urge to understand everything — and the frustrations it can bring. In his case, he has attempted to master every major literary form, with perhaps most success — until the publication of Sentenced to Life — in the personal essay.

James has approached the time of his vanishing with grace and good humour, not sentimentality or anger. These essays and poems are death-haunted but radiant with the felt experience of what it means to be alive, even when mortally sick, especially when mortally sick.

He does not believe in an afterlife. We have only this one life, as he sees it, and his is ending. “We won’t be taking our knowledge any further,” he writes, “but it brought us this far.” For now, he lives and so he works, for as long as he can, for as long as time will allow.