His father died when he was just aged two and was raised by his mother Malvina Marian (née Schlesinger) and her older sister who had moved to live in Hampstead, London.
By 1901 the family moved to Kensington and Martin began to work as a bank clerk for a while and took an interest in fishing, possibly through Frederic M. Halford (1844-1914).
Mosely was admitted as a Fellow of the Entomological Society of London in 1910, proposed by Malcolm Burr and seconded by Kenneth J.
He began to work on it but was interrupted by World War I. Mosely volunteered with the East Surrey Regiment and then the Royal Fusiliers.
After the war, the book plan was hindered by high costs and the lack of an artist to produce the plates.