Outside the window of Tate Liverpool the wind is whipping up a storm. The Mersey is a steely, inhospitable grey, and the clouds are louring. Indoors, the veteran English pop artist Peter Blake, creator of the cover art for the Beatles’ Sgt. Pepper album, who is having his first major painting retrospective in a quarter of a century, seems to be alive in quite a different sort of climate.

On a wall panel, he explains what has inspired his latest series of paintings in homage to Marcel Duchamp, that Frenchman who almost 100 years ago displayed a pristine white urinal inside a museum and declared it art. “I decided to send him on a posthumous world tour, rather like the Flying Dutchman,” Blake burbles merrily, “where he would travel the world forever in a big rock‘n’ roll tour bus. He meets people along the way, and people come and go on the bus, and he goes to various happenings.”

In one, Duchamp meets Picasso, mysteriously reincarnated as Touchstone from Shakespeare’s As You Like It, while the brooding American painter of Nighthawks, Edward Hopper, stands near by. In another, Duchamp is playing chess with Tracey Emin, while in a third he meets members of Barnum and Bailey’s circus – the bearded woman, the fat lady.

This is Peter Blake as we have always known him, the genial mixer and matcher of high and low culture, who from the 1960s onwards has produced pop art of a particularly English and nostalgia-soaked kind. The man who loves popular entertainment, from wrestling to rock‘n’roll, has always seemed to be a pop artist without any real hint of menace. A playfully innocent observer and recorder of his own enthusiasms, he is a painter to be enjoyed, but one who lacked much challenge or edge. Where Warhol produced lithographs of electric chairs and car crashes in glarily eerie tones of green and pink and yellow, Blake, at worst, gave us a few racy pin-up girls.

But is it really that simple?

In this show we see an aspect of Blake that we had scarcely glimpsed before – a painter more sober and perhaps more anxious than we had imagined. In short, a painter of some real psychological depth, if only fitfully.

The earliest paintings in the show, mostly portraits of children, are the key to it all. Blake was an evacuee from London during wartime and these early images, such as Boy and Pigeons from 1954, have a haunting and a haunted quality. Heads loom large within the picture frame; eyes glare back at us. It is as if the very souls of these children reside in their searching looks. There is a yearning for something irretrievably lost, something paradisal perhaps.

On an adjacent wall hangs one of Blake’s most famous paintings, Self Portrait with Badges, of 1961, and we begin to read it differently in the light of these strange and engaging early portraits. Although his paintings have always seemed to epitomise the 1960s, culminating with the Sgt. Pepper album cover of 1967, he seems less at home in this self-portrait than we might have thought. Blake was not an especially young man at the beginning of the 1960s – he would have been 30 in 1962. There is an almost Larkin-like awkwardness and gaucheness to the man in this portrait. The badges on his jacket look like so much ridiculous clutter; the Elvis fanzine hangs limp in his hand.

The show then rockets us through the rest of the 1960s. Blake makes repeated homages in painting to friends and heroes – Bo Diddley, the Beatles, Marilyn, Elvis. This is an art of joyful incorporation – of postcards, toys, record sleeves. In works that are part sculpture and part collage he stuffs in as much popular culture as possible because he just loves the stuff. But while his works seem in part to belong to the fairground, he is also in love with the newest avant-garde imports from America – postpainterly abstraction, for example.

The problem is that so much of this work seems to be slightly off the boil – pictorially interesting, but not that interesting; based on photographs, but not much more accomplished or engaging than the photography it uses as its source material.

Then, in 1979 something happens again. Blake had lost himself for years to a kind of nostalgia for the mystical values of the English countryside: during the 1970s he and a group of friends left London for the West Country and called themselves the Ruralists. But then, with his old friend Howard Hodgkin, he makes a visit to another mate called David Hockney in Los Angeles. As a consequence of that visit he paints a picture called The Meeting, or Have a Nice Day, Mr Hockney. It is the greatest painting of his life – tonally and compositionally; in its extraordinary use of light and colour. Hodgkin and Blake meet Hockney on the boardwalk. Hockney looks relaxed and Californian. He carries a giant paint brush. Blake greets him, arms flung out, with an absurd degree of ceremony.

The composition is derived from a painting by Chardin, but it is entirely Blake. It is as crisply realistic as those early portraits of children but it also suffused with a quality of profound and endearing fantasy. It feels as if the two sides of Blake have come together – that ever playful “voyeur of life’s goings-on”, as he described this visit to California, and the man who stared so deeply into the eyes of those children.

— Peter Blake: A Retrospective is at Tate Liverpool (0151-702 7400) from Friday until Sept 23

Editor's choice

• The super cool Vampire Weekend
• Streep and Baldwin get complicated
• Guy Ritchie on Sherlock Holmes