Memoirs, one of Hodgkin's earliest recorded paintings, shows the artist, then aged 17, listening to a female figure reclining on a sofa. Painted with angular forms and black outlines, the work precedes Hodgkin's distinct abstract syle. Hodgkin's first solo show was in London in 1962. In 1980, Hodgkin was invited by John Hoyland to exhibit work as part of the Hayward Annual at the Hayward Gallery along with Gillian Ayres, Basil Beattie, Terry Setch, Anthony Caro, Patrick Caulfield, Ben Nicholson and others. In 1981, Hodgkin had collaborated with the Rambert Dance Company's Resident Choreographer, Richard Alston, for his abstract work 1981 for the production of Night Music and later for the production of Pulcinella in 1987. In 1984, Hodgkin represented Britain at the Venice Biennale, in 1985 he won the Turner Prize, and in 1992 he was knighted.
Hodgkin was invited to design a mural for the front of Charles Correa's 1992 headquarters for the British Council in India. Hodgkin's mural is of a banyan tree spreading its branches across the walls. It is a symbol of the British Council's work rooted in the Indian cultural scene. Hodgkin said of Correa: “Charles Correa is the most perfect architect you could imagine. He first suggested that I think about the mural as an Indian flag turning into a Union Jack. I said no.” In 1995, Hodgkin printed the Venetian Views series, which depict the same view of Venice at four different times of day. Venice, Afternoon – one of the four prints – uses 16 sheets, or fragments, in a hugely complex printing process that creates a colourful, painterly effect. This piece was given to the Yale Centre of British Art in June 2006 by its Israeli family owners in order to complement the museum's already-impressive collection of Hodgkins. A major exhibition of his work was mounted at Tate Britain, London, in 2006. Also in 2006, The Independent declared him one of the 100 most influential gay people in Britain, as his work has helped many people express their emotions to others. In September 2010, Hodgkin and five other British artists, John Hoyland, John Walker, Ian Stephenson, Patrick Caulfield and R.B. Kitaj, were in an exhibition entitled The Independent Eye: Contemporary British Art From the Collection of Samuel and Gabrielle Lurie, at the Yale Center for British Art. Delhi Headquarters, launch of Mix The City, 6 April 2017 Before his death on 9 March 2017 he was working on two UK exhibitions, one at the Hepworth Wakefield, and another at the National Portrait Gallery. His prints were hand-painted etchings and he worked with the master printer Jack Shirreff at 107 Workshop. A feature of his painting was that he made the frame intrinsic to the work " incorporated physically into the painting as part of its making, or created as an illusion to give definition to his subject." National Life Stories conducted an oral history interview with Howard Hodgkin between 2008 and 2017 for its Artists' Lives collection held by the British Library.
In 1955, Hodgkin married Julia Lane, by whom he had two children. Hodgkin knew he was gay, even when he was married, and later left his wife. In 2009, The Independent reported that he had been with his partner, the music writer Antony Peattie, for 20 years. They lived in a four-storey Georgian house in Bloomsbury, near the British Museum. On 9 March 2017, Hodgkin died at the age of 84 in a hospital in London. Tributes to him were made by several figures in British art, including Tate director Nicholas Serota.