Pop Art didn’t exist when Richard Hamilton helped to organise the epoch-making London exhibition This Is Tomorrow, held at the Whitechapel Art Gallery in 1956. But his section of the show was daring enough to celebrate images culled from advertising, comic books and film publicity. It outraged conservative English opinion at the time, and Hamilton also made a brilliantly witty, provocative collage called Just what is it that makes today’s homes so different, so appealing?.

Here, in a room containing a blown-up cover of Young Romance and an immense tin of ham on the coffee-table, a muscle-bound Mr Universe flaunts his physique and clasps a shamelessly phallic tennis racket. It thrusts out of his groin like a giant lollipop, and the words “Tootsie POP” are splashed across its orange wrapping paper.

Looking at this collage now, we immediately link Hamilton with the brash images produced in New York by Roy Lichtenstein and Andy Warhol. But they did not begin their Pop work until the 1960s. Hamilton was a prophet, and his innovative collage now looks like a clarion call for the army of Pop artists who would take the Sixties by storm. His prodigious career is about to be celebrated in a major retrospective show at Tate Modern, which opens this week. But back in 1956 he was struggling to make a living. I was lucky enough to interview Hamilton on several occasions and once asked him how he had felt then, as a 34-year-old artist in London. “I felt completely out on a limb”, he told me. “I thought that I was being tremendously adventurous and alone, going out into the sea with absolutely nothing in front of me.”

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At this difficult stage in his career, Hamilton benefited from belonging to the Independent Group, a “small, cohesive, quarrelsome, abrasive” assembly of angry young artists, critics and theorists who met regularly at the ICA in London. He felt stimulated by the intense, questioning attitude which gave these meetings their extraordinary vitality. For Hamilton had always been a rebel, right back to his time studying at the Royal Academy Schools. His experiences there ended in an explosive rumpus, and he relished telling me about it many years later.

Hamilton first entered the RA Schools in 1938, when he was only 16. At first the precocious teenager did well, but the Schools were closed during the Second World War. Hamilton recalled that “I had to go to the Labour Exchange, and they said: ‘What have you been doing? Can you use a pencil? We’ll make you an engineering draughtsman.’” So Hamilton received training and worked for a few dull years in an armaments factory. When the war ended, he returned with immense relief to the RA Schools. But the reactionary teachers hated Hamilton’s fascination with Modernism.

“Alfred Munnings had become the President, and he used to appear after riding in Rotten Row”, Hamilton told me. “Dressed in a rakish hat and boots, with a riding crop in his hand, he would shout: ‘Are you one of those bastards who talks about Picasso?’ Munnings was frightening, and my teacher Thomas Monnington also got angry when he saw my Cézanne-influenced life drawings. He said: ‘Augustus John knocks spots off Cézanne!’ I roared with laughter – it was hysterically funny. But Monnington was not amused.”

Hamilton refused to change his ideas about art. “By that time I wasn’t a kid any more, and this was all a bit silly. Sir Walter Russell, the Keeper of the RA Schools, was still kind to me, but he called me in and said: ‘The President has been told that you are not profiting from your studentship. Therefore it is terminated.’ I was expelled.” At the age of 24, the would-be artist now found himself “dragged screaming into the bloody Army for a year-and-a-half’s national service with the Royal Engineers”.

Hence Hamilton’s eagerness to be defiantly innovative when he resumed his own creative work in the 1950s. But even after the exposure afforded him by This Is Tomorrow, he “tried for eight years to persuade dealers around London to give me an opportunity to show.” Then, quite suddenly, he said, “I learned about the existence of Peter Blake, Allen Jones and David Hockney”. They were still students at the Royal College of Art, but Pop Art now created enough excitement to earn them a show in London. Even though Hamilton was over a decade older than most of them, he felt “very pleased that I was invited to contribute” to this exhibition. “I was carried along on David Hockney’s golden coat-tails. He wafted in, and I was somehow given a little reflected shine from this gold suit that he wore on special occasions.”

During the 1960s, Hamilton revealed just how impressive and experimental he really was. References to the cinema abound in his work from this period, but its tone ranges from the brashly satirical to the profoundly mournful. The leader of the Labour Party is transformed into a bug-eyed maniac in Portrait of Hugh Gaitskell as a Famous Monster of Filmland. But in the same year, 1964, Hamilton explored his preoccupation with death by producing the sinister Interior II, based on a murderous moment in the 1949 thriller Shockproof. Then, a few years later, he seized on a press photograph of a contemporary event: Mick Jagger’s notorious arrest on a drugs charge alongside the art dealer Robert Fraser. Handcuffed together in a police van, the two men raise their hands in an ambiguous gesture – half demonstrating their plight, half shielding themselves from intrusive cameras. And Hamilton chose a typically sardonic title for his picture: Swingeing London 67.

As he grew older, harrowing themes dominated his work. The tragedy of Northern Ireland haunted him, especially when he saw a TV news film of the so-called Dirty Protest at The Maze prison near Belfast. In The Citizen, he showed the Christ-like figure of a bearded protester who wore blankets and smeared the walls of his cell with excrement. Hamilton was also profoundly moved by the fatal shooting of four students by National Guardsmen at Kent State University, Ohio, during a campus demo in 1970. “It’s a demonstration of the stupidity of mankind”, Hamilton told me in 2010, his voice still expressing the deep emotion which had led him to make such a powerful work from the event.

By then he was approaching 90, but still completely dedicated to producing art at the Oxfordshire farmhouse where he lived with his wife and fellow-artist Rita Donagh. “I have a very fine lamp hanging over my easel”, he said. “Rita gets fed up with me if I’m not ready for my gin and tonic by half-eight or nine. But it’s necessary to work a lot, in spite of the pain from my arthritis. I’m getting on, and I don’t recommend it!” He died in September 2011, and only now will the Tate Modern exhibition, along with related shows at the ICA and the Alan Cristea Gallery, reveal the full extent of his multi-faceted achievements.

Tate Modern’s Richard Hamilton retrospective runs from Thursday to 26 May