Kennington was born in Chelsea, London, the second son of the well-known genre and portrait painter, Thomas Benjamin Kennington (1856-1916), a founder member of the New English Art Club. He was educated at St Paul's School and the Lambeth School of Art. Kennington first exhibited at the Royal Academy in 1908. At the International Society in April 1914 Kennington exhibited a series of paintings and drawings of costermongers which sold well and allowed him to set up a studio off Kensington High Street in London.

Kennington enlisted with the 13th (Kensington) Battalion London Regiment on 6 August 1914. He fought on the Western Front, but was wounded in January 1915 and evacuated back to England. He spent six months painting The Kensingtons at Levantie, a group portrait of his own infantry platoon.

When exhibited in the spring of 1916, its portrayal of exhausted soldiers caused a sensation. Painted in reverse on glass, the painting is now in the Imperial War Museum and was widely praised for its technical virtuosity, iconic colour scheme, and its "stately presentation of human endurance, of the quiet heroism of the rank and file". (Paul Gough (2010). A Terrible Beauty: British Artists in the First World War.)

Kennington visited the Somme in December 1916 as a semi-official artist visitor before, back in London, producing six lithographs under the title Making Soldiers for the Ministry of Information's Britain's Efforts and Ideals portfolio of images which were exhibited in Britain and abroad and were also sold as prints to raise money for the war effort. In May 1917 he accepted an official war artist commission from the Department of Information.

Kennington was commissioned to spend a month on the Western Front but he applied for numerous extensions and eventually spent seven and a half months in France.

In 1946 Kennington was appointed as the official portrait painter to the Worshipful Company of Skinners. Over the next five years he produced nine pastel portraits for the company, which were highly praised when shown at the Royal Academy. In 1951 Kennington became an associate member of the Academy and was elected a full academician in 1959.