The son of a professional painter of birds and flowers and a Welsh mother, Dobson's earliest art training was at the Leyton School of Art (1900-02) after which he was apprenticed to the sculptor Sir William Reynolds-Stephens for two years.

In Cornwall (1904-06) 'I had practically no contact with other artists. I spent most of my time in painting and sketching that very lovely country and my spare time in swimming and sailing.' (He did, however, produce landscapes under two assumed names, as mentioned below, for his livelihood).

From 1906-10, having heard by chance in Cornwall of the Hospitalfield Art Institute in Arbroath, Scotland, he applied for and received a scholarship there, where he worked on his teaching methods and visited the Glasgow Institute, becoming 'gloriously drunk' on Monet and Pissarro before returning to London for further practice in drawing and modelling.

From 1910-12 he attended the City and Guilds School, Kennington after a brief abortive attempt to study with a disapproving Stanhope FORBES (who did not like his palette of colours) in Newlyn. He returned to Cornwall in 1913-14 as it afforded a cheaper place to work, and shared a studio at Newlyn with Cedric MORRIS. Here he painted oils and made his first sculpture, working with a local stone mason. Here, also, he met Augustus Edwin JOHN for the first time.

After active service in WWI (during which he also drew and painted) he returned to Cornwall in 1919, and married Cordelia Johnson, sister of the artist, Mary JEWELS, and they returned to a busy social life amongst artists and writers in London. Through a friend in Cornwall (Capt Guy Baker), he was introduced to Wyndham LEWIS, and later exhibited with Group X in 1920. As a sculptor, his first solo exhibition was held at the Leicester Galleries in 1921.  During WWII he became an official war artist in 1940.

From 1946 to 1953 he was Professor of Sculpture at the Royal College of Art.

Inscriptions include: Dobson; F Dobson; F O Dobson; FOD; F Dobson and title; F Dobson with number.