Henry was born in Southwark, London. He was educated at Tonbridge School from 1893 to 1898. After school he studied at art schools in London and Paris. He became a member of the Royal Society of British Artists and was appointed as an official guide of the National Gallery of British Art (now called Tate Britain).

As a painter he was particularly successful in interpreting the life and beauty of the Thames at London. He exhibited at the Royal Academy, the Royal Society of the British Arts and in the Goupil Gallery. His painting, Down the Thames, is dated 1913 and is one of a number featuring the working life along the river. In 1914 he was elected to the position of art director of the Whitechapel Art Gallery. On 25th July 1914, he married Marguerite Kate Lila Wiffen, of Vancouver, Canada. 

He joined the Inns of Court Officer Training Corps in May 1915 and was commissioned into the Royal Berkshire Regiment on 6th August 1915. He went to France on 7th January 1916.

He was killed in action on 24th July 1916, aged 33, during an attack on the village of Pozières.

A brother officer, writing to express his sympathy with Mrs. Teed, said, '…He was shot by a German sniper while gallantly observing the effect of our hand and rifle grenades. Always a dangerous job, it was more than ever so on that occasion, as the enemy’s snipers must have been close up behind their bombing party, which had, at one point, just entered our trench…'

The Pall Mall Gazette of 2nd August 1916, reported,

'…Teed was a whole-soul painter, particularly sensitive to certain aspects of landscape and architecture. It was characteristic of his thoroughness that he lived for five years in a curious old house in the bargee quarter of Bankside, where the finest view of St. Paul’s can be seen. From his broad window there he painted the dome and the river in all its changeful aspects through the seasons of the year. Probably no one knew the variety of beauties which flowered in that majestic grouping of river and dome and clouds as the artist who is just gone…'

 Some of his works were posthumously featured in the 1916 Autumn Exhibition of the Royal Society of British Artists.