Pegram was born in London and received his first artistic education at the West London School of Art. Already in 1881 and in 1883 he won prizes at the National Art Competitions. In 1881, he entered the Royal Academy schools, where he again won prizes in 1882, 1884, and 1886. In 1887 he left the school and worked until 1891 as assistant to Hamo Thornycroft. He became a member of the Art Workers' Guild in 1890, an Associate of the Royal Academy in 1904 and finally a Royal Academician in 1922. From 1890, Pegram was commissioned for numerous building decorations and statues. In 1913, he was one of the ten sculptors selected to work on the city hall of Cardiff, for which he sculpted the figure of Llewelyn the Last.
His daughter, Doris Joan Pegram, married the artist and illustrator H. M. Brock.
Henry Alfred Pegram died in 1937 in his home in Hampstead, London.
Prizes
Bronze medal at the Paris International Exhibition of 1889 (for Death Liberating a Prisoner)
Gold medal at Dresden, 1897 (for The Last Song)
Silver medal at the Paris International Exhibition of 1900 (for a life-size plaster cast of Sibylla Fatidica, a marble version was presented in 1904 to the Tate.)
Selected works
Industry and Britannica, entrance of the Imperial Institute, London. (1891–1892)
Ignis Fatuus or Misleading Light (1889).
The Last Song (1897).
Bronze candelabra in St. Paul's, London (1897).
Sibylla Fatidica (1900–1904).
Monument to Ninon Michaelis at Kensal Green Cemetery (approx 1901).
Reliefs at St Paul's Girls' School, Brook Green. (1903)
"The Bather" friezes at Buckingham Gate no. 20, Westminster, London (now the High Commission of Swaziland).