It is a book in which one man, living in a totalitarian society a number of years in the future, gradually finds himself rebelling against the dehumanising forces of an omnipotent, omniscient dictator. Encouraged by a woman who seems to represent the political and sexual freedom of the pre-revolutionary era (and with whom he sleeps in an ancient house that is one of the few manifestations of a former world), he writes down his thoughts of rebellion – perhaps rather imprudently – as a 24-hour clock ticks in his grim, lonely flat. In the end, the system discovers both the man and the woman, and after a period of physical and mental trauma the protagonist discovers he loves the state that has oppressed him throughout, and betrays his fellow rebels. The story is intended as a warning against and a prediction of the natural conclusions of totalitarianism.

This is a description of George Orwell's Nineteen Eighty-Four, which was first published 60 years ago on Monday. But it is also the plot of Yevgeny Zamyatin's We, a Russian novel originally published in English in 1924.

Orwell's novel is consistently acclaimed as one of the finest of the last 100 years – two years ago Guardian readers voted it the 20th century's "definitive" book – and it remains a consistent bestseller. Should it alter our respect for it that Orwell borrowed much of his plot, the outlines of three of his central figures, and the progress of the book's dramatic arc from an earlier work?

Orwell reviewed We for Tribune in 1946, three years before he published Nineteen Eighty-Four. In his review, he called Zamyatin's book an influence on Aldous Huxley's Brave New World, though Huxley always denied anything of the sort. "It is in effect a study of the Machine," Orwell wrote of We, "the genie that man has thoughtlessly let out of its bottle and cannot put back again. This is a book to look out for when an English version appears." He seems to have taken his own advice.

We was not published in Russia until the glasnost era of 1988; among its most controversial passages for the Soviets was an apparent call for a new revolution to sweep away theirs: "How can there be a final revolution? There is no final one. The number of revolutions is infinite. The last one – that's for children. Infinity frightens children, and it's essential that children get a good night's sleep." Foreign editions released in Zamyatin's lifetime led to his being banned from publishing, and eventually he wrote to Stalin to ask permission to live abroad. It was granted, and he left Russia for ever in 1931. He died six years later.

The characters in We are numbered rather than named: its Winston Smith is D-503, and its Julia I-330. Its Big Brother is known as the Benefactor, a more human figure than Orwell's almost mythical dictator, who at one point phones D-503 ("D-503? Ah … You're speaking to the Benefactor. Report to me immediately!"). Where Orwell's apartments come complete with an all-seeing "telescreen", Zamyatin's buildings are simply made of glass, allowing each of the residents – and the "Guardians" who police them – to see in whenever they want. We's Airstrip One, or Oceania, is called OneState. Instead of puzzling over 2+2=5, its lead character is disturbed by the square root of –1.

There are many aspects of We that mark it out as an interesting work in its own right. Zamyatin has a distinctive way with description: when a doctor laughs, "the blades of [his] scissor-lips flashed", while a woman walks along moving her buttocks "from side to side as if she had eyes in them". He anthropomorphises the letters that begin his characters' names; it is thought he may have had synaesthesia, and identified letters with certain colours.

On the down side, Zamyatin's structure – a series of diary entries – becomes progressively less believable the more trouble D-503 gets himself into, while his plot is marred by confusing jumps in time and place. A scene in which the characters fly into space unfortunately cannot help but seem laughable now.

So does it matter that Orwell borrowed plot and characters from the earlier book? After all, it seems clear that he made a superior work of literature out of them. Nineteen Eighty-Four's importance comes not so much from its plot as from its immense cultural impact, which was recognised almost immediately when it won the £357 Partisan Review prize for that year's most significant contribution to literature, and which has continued to this day. Most of the aspects and ideas of the novel that still resonate so strongly in political life are his own: newspeak, doublethink, thoughtcrime, the Thought Police, Room 101; the extreme use of propaganda, censorship and surveillance; the rewriting of history; labels and slogans that mean the opposite of what they say; the role for Britain implied in the name Airstrip One. References to these things pervade all levels of our culture. Apart from the obvious, I remember an amusing NME review of an album by the laddish band Cast that read: "Imagine a trainer stamping on a human face ... for ever."

In addition, unlike We, Nineteen Eighty-Four is written with expert control in an accessible style about a world recognisably our own, and its twists of plot – including the existence (or not) of the Brotherhood resistance movement – are gripping, sophisticated and convincing. The dark, pessimistic tone of Nineteen Eighty-Four is also all Orwell's.

If any aspect of We takes the shine off Nineteen Eighty-Four, it's that Orwell lifted that powerful ending – Winston's complete, willing capitulation to the forces and ideals of the state – from Zamyatin. It's a wonderful, wrenching twist, in both books, and a perfect conclusion, though We and Nineteen Eighty-Four differ slightly in the fate of the female dissident: I-330 is killed without giving up her beliefs, whereas Julia is broken in the same way as Winston.

Perhaps We deserves more recognition than it has had, but if Nineteen Eighty-Four had never existed, it is extremely doubtful Zamyatin's book would have come to fill the unique place Orwell's work now occupies. Nineteen Eighty-Four is an almanac of all the political ideas no "right-thinking" person would ever want their government to countenance, and the word Orwellian has come to signify a badge of shame intended to shut down any movement in that direction – with an imperfect record of success.