As television news tributes have said, Ian Holm is best known for his performances in the films Chariots of Fire and Lord of the Rings. But to me, the name Ian Holm stands for something altogether different. For me, he is the genius who invented contemporary Shakespeare acting.

As the close-up naturalism of film and television became the staple expression in the 1960s, the danger was that Shakespeare stage performance would be increasingly seen as rhetorical, bombastic, external and, in the pejorative sense, theatrical.

Emerging into prominence in the early work of the Royal Shakespeare Company, he played Prince Hal in the two parts of Henry IV and then, in the greatest challenge of his career to that point, Henry V. The postwar definitive Henry had been filmed and played by Laurence Olivier, in a production that proclaimed the play to be the national anthem in five acts. Olivier’s vocal range and pyrotechnics were thrilling, but essentially, the performance was a recitation of a famous verse text.

Unforgettably, Ian Holm’s Henry – youthful, out of his depth, full of self-doubt – transformed that famous text into something we had never heard and never experienced before. He was able to convince us that what he was saying was the spontaneous expression of his thoughts, in language that was summoned up from within him. There was no hint of recitation. No hint that anything he was saying had ever been written down before. He was as real as filmic, close-up naturalism could ever be.

I was witness to this revelation as assistant and finally co-director of that production. Ian Holm transformed the role, he transformed Shakespeare acting, he transformed the acting of the company around him, he transformed the English theatre for decades, as only an actor of genius could. May his influence never wane.

• Trevor Nunn is a theatre director and was previously artistic director of the Royal Shakespeare Company and the Royal National Theatre