The Waste Land is being reissued on the 50th anniversary of TS Eliot's death

As a child, I was handed anthologies like James Reeves's The Rhyming River, where I encountered Edward Lear and Lewis Carroll. One Christmas I received TS Eliot's Old Possum's Book of Practical Cats, which I loved reading aloud. Much later I recognised it as Eliot's workout book for formal and rhythmic dexterity, but meanwhile Macavity and Skimbleshanks the Railway Cat took up residence in my imagination and my hearing, along with the melancholy of Lear's "Dong with the Luminous Nose" and "The Jumblies". We recited the last of these in infant school.

My mother was a headteacher and I also browsed in the publishers' inspection copies that arrived in her office. The sum of this reading was both very English and in some ways strange to the point of madness (think of Lear; think of Carroll). So when Eliot's poems for adults appeared in the classroom in my teens, with his foggy evenings, his smoke-dimmed secret streets and the sense of something not quite being said, the sound and the landscape seemed almost familiar, like a musical district hitherto hidden round the corner from where I lived.

Eliot, I learned, was American but had somehow made himself English. I was hooked and carried on reading. By the time my A-level group encountered The Waste Land as background reading I viewed it as my personal property. It was the flagship of poetic modernity, published in 1922, consisting of 433 lines (after Ezra Pound had taken his blue editorial pencil to it), plus notes. It was difficult, secret, multilingual and non-linear: ergo it was interesting, and, though I couldn't have said so at the time, it satisfied Seamus Heaney's requirement for poets to make a unique "noise":

"I was fishing in the dull canal

One winter evening round behind the gashouse

Musing upon the king my brother's wreck

And on the king my father's death before him."

This is characteristic – the blending of the grimy modern city and The Tempest, underscored by that strangely neutral music, through which the iambic metre surfaces from time to time, and for which the present occasion is only ever part of a larger composition.

The Waste Land and much of Eliot's other poetry has been part of the soundtrack of my life. His auditory inspirations are as many as his allusions, including the Bible, Buddhist scripture, Dante, Shakespeare and the whole of European literature, as well as ragtime and vaudeville from his native St Louis, and the English music hall, and what people could be heard saying in the streets and pubs of London. A particular pub comes to mind. In 2008, 40 years after first reading The Waste Land, I stood outside Crawford Mansions in Marylebone. In the presence of the Mayor, Valerie Eliot was dedicating a plaque to a famous former resident. Eliot had lived here with his first wife, Vivienne Haigh-Wood, in this red-brick block opposite a pub where we went afterwards. Mrs Eliot sat quietly nearby with a companion.

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After an hour we all went our ways and the world was unaltered. But re-reading The Waste Land now, I go back to lines from Part Three, "The Fire Sermon": "On Margate Sands. / I can connect / Nothing with nothing." Biographical readings of poems so often miss the point, ie, the poem, in favour of reductive explanations of its supposed origins. But Eliot's case seems an exception. Imprisoned by coupledom, stalked by madness, one of the speakers in The Waste Land says:

"My nerves are bad tonight. Yes, bad. Stay with me.

Speak to me. Why do you never speak? Speak."

It does sound like an evening with Eliot and Vivienne, gruellingly described in Robert Crawford's biography Young Eliot. Later on, time is called in the nearby pub, during a brutally uninhibited female conversation about an abortion:

"You are a proper fool, I said.

Well, if Albert won't leave you alone, there it is, I said.

What you get married for if you don't want children?"

The juxtaposition is Shakespearean: on the one hand the neurotic and genteel, and on the other working class frankness. It forms, as the poem puts it, "that Shakespeherian rag", and like Shakespeare Eliot is able to place a multitude of particular lives and voices and languages so that they embody a general condition. In this case a psychic and cultural crisis where the entire resources of artistic and cultural tradition cannot put the world together again.

Yet in a sense the poem overcomes its disconnections by naming them. Derek Mahon's "Lives" ends with advice to whoever knows too much: "Let him revise / His insolent ontology / Or teach himself to pray", and it's in prayer, of a kind, that The Waste Land closes.

It was strange to be sitting across the road from a private tragedy. Whatever Eliot's widow may have thought as she sat there, elderly and in failing health, she did not of course disclose. As for the pub itself, it had no doubt seen all sorts of people and things in its time: for a pub, in Douglas Dunn's words, "We are small loss / To its varnished eyes." But, just then, its placid mid-afternoon quiet and perfect ignorance did reinforce Eliot's point about the "essential horror" of human affairs.

It seemed a long way from Practical Cats but it was, inexplicably, incredibly, part of the same world, the world Douglas Dunn described as "Sensible, commonplace, beyond understanding". Eliot was essentially a dramatic poet, and his poems are events of the imagination. As we begin to read "April is the cruellest month", the poem begins to happen.

Poetry is one of the few ways of preventing the waters of unreflective ordinariness and deathly common sense from closing over us, of reconnecting links that seem broken and, whether we like it or not, of speaking to our condition. The Waste Land is a major example of its powers.

Sean O'Brien's latest poetry collection, 'The Beautiful Librarians' (Picador), is out now