James Gleeson is not for sissies. His work is disturbing, sometimes terrifying, but always thought-provoking. His compelling images have a terrible beauty that fascinates even as it repels.

Gleeson himself said that he has never believed that art should be limited to "what is conventionally considered beautiful … I think art should be all-embracing: it should cover every aspect of existence and that includes what you technically call ugliness, terror, fear and anxiety. I think it's all part of life. I was born in the second year of the First World War; then there was the atmosphere of the '30s when you knew there was going to be another war. The idea of war and destruction has always been part of existence."

I spent a morning at the exhibition – took time out now and then for a restorative dose of caffeine and a chocolate biscuit which the girl in the cafeteria assured me had negative calories. Thus fortified, I could go back for another dose of the strange and beguiling world of James Gleeson.

During the 1940s, his work was imbued with images of war and violence. "The Sower" (1944) and "The Citadel" (1945) were two paintings from this period that I found particularly powerful. The former is a nightmare of distorted body parts, dragon heads, skulls and jagged, toothlike rocks: flesh, scales and rock are all rendered in tones of brown and grey and seem to be of the same substance. I was reminded of the Greek myth of the fierce, cruel warriors who sprang from the earth when dragons' teeth were sown. Indeed, religion and Greek myth informed a lot of Gleeson's later work..

I imagine that the title must refer to the prophet Hosea's strictures on the Israelites' warring with the neighbours: "For they have sown the wind, and they shall reap the whirlwind." (Not a lot has changed in two thousand years!)
 

Apocalyptic as "The Sower" is, "The Citadel" is more fearsome. I found myself coming back to the picture several times: the lurid images of mutilated body parts and an eye rimmed with teeth exert a hideous fascination. Rotten teeth chew on an arm, intestines are draped over mounds of cancerous flesh and horrid spiky plants grow at the base, like Triffids feeding on the corruption. The artist seems to say that the wholesale killing in war is just humanity cannibalising itself.

I stood there quietly like a rabbit caught in the headlights – the woman next to me was muttering "Whooo, whooo…" and feebly waving her hands like someone practising the breaststroke. She obviously needed a negatively geared chocolate biscuit to bolster her resolve.

In 1947 Gleeson went abroad and absorbed the works of the old masters. His work in the 'fifties was inspired and influenced by what he saw, and also by myth, religion, poetry and history. One recognises the influence of Turner in the glowing light effects that he uses in some works. In others, the colossal figures, dark, looming skies and an aura of menace echoed Goyas I have seen in the Prado: "The Colossus" of war looming over a Spanish village and "Saturn devouring his children" exude that same air of dread and impending doom.

Gleeson pays homage to the great Surrealists too: there were several works that were very reminiscent of Magrittes I'd seen in Antwerp's Stadsmuseum: meticulously drawn everyday objects in an extraordinary context: the "magic realism" that Magritte pioneered. Indeed, Gleeson also echoed Magritte's trick of creating surrealist versions of famous paintings: I was amused by a large canvas called "Faux Delft by day/night" …

When I first looked at it, it seemed so familiar, yet I knew I had never seen it before. Then it dawned on me that I was looking at Vermeer's "View of Delft", rendered surrealistically! Instead of the Dutch ladies in the foreground, Gleeson had painted himself at his easel. He used the same palette of colours and kept the skyline similar, although Vermeer's buildings are now bottles and pelicans and weird animals, with the same silhouettes. I like a painter with a sense of humour!

Not all the pictures were the stuff of nightmares: there were some extraordinarily beautiful works. I was delighted by "Clouds of witness" (1966), in which nude figures are floating in clouds and in water, tucked into niches and reclining on beaches, all among swirls of luminous gold, white and blue.
 

He incorporates self-portraits in some of his works, and says that he never paints anyone else: he did a portrait of his sister once, but it is not good to paint other people, "because they are never satisfied. If you  paint only yourself, you have only yourself to satisfy."