David Hockney’s first English landscape, depicting a perfectly manicured Oxfordshire garden, is on show for the first time in three decades before being auctioned.

Sotheby’s said the 1965 painting, English Garden, which was completed in Boulder, Colorado, was pivotal for Hockney as well as holding an important place in wider art history.

“It is a seminal painting,” said the Sotheby’s co-head of contemporary art in London, Tom Edisson. “It really lays the foundations for everything that was to come after.”

The painting has gone on display at the auction house’s central London galleries before its sale on 4 March, with an estimate of £2.5m-£3.5m.

Hockney was not long out of art school when he moved to the US, and in the summer of 1965 he was invited to teach at the university in Boulder, Colorado.

He found himself a lover, a 19-year-old student called Dale Chisman, and enjoyed his six weeks in Boulder but was given a studio with no windows.

“Here I am surrounded by these beautiful Rocky mountains,” he told his biographer. “I go into the studio – no window! And all I need is a couple of little windows.”

Looking for inspiration, he came across a photograph in American Vogue by Horst P Horst of a sculptured topiary garden at Haseley Court, Oxfordshire, home to the designer and tastemaker Nancy Lancaster.

Edisson said: “You have a pang of nostalgia, maybe a bit of homesickness, looking back at England’s green and pleasant lands … I think that spurred him on to paint home.”

English Garden is Hockney’s first fully realised English landscape and was painted at a time when abstract art, not figurative, was the dominant force.

Edisson said the work was particularly exciting “because it cements so much of what we know Hockney’s practice is about and what we’ve all come to love about him as an artist … it was a real turning point.”

Outside his California pool paintings, Bradford-born Hockney’s more recent paintings of the East Yorkshire landscape are among the most recognised and best loved paintings of his career, said Edisson.

The direct link can be seen in English Garden, he added.

The painting was exhibited at Kasmin Gallery in London in the year it was painted and last went on display in a public gallery in a 1970 show at the Whitechapel Gallery in London. It has been in private hands since, appearing at auction in 1997.

Hockney, now 88, remains busy, with an exhibition of new works opening at the Serpentine Gallery in London in March.

It follows the largest ever Hockney show last year, when more than 400 of his works were exhibited at the Fondation Louis Vuitton in Paris where, Edisson said, visitors could see the scale of the artist’s ambition and his “extraordinary” drive.

“He is constantly challenging himself. He is still at the forefront of contemporary art and this painting [English Garden] is to me the root of everything that came after.”