In parallel with his RGS duties Markham served as secretary of the Hakluyt Society until 1886, subsequently becoming that society's president. As part of his work for this body, Markham was responsible for many translations from Spanish into English of rare accounts of travel, in particular those relating to Peru. In time scholars would express doubts about the quality of some of these translations, finding them prepared in haste and lacking in rigour. Nevertheless, this work ran to 22 volumes in the society's publications. In 1873, Markham had been elected a Fellow of the Royal Society, and in subsequent years received several overseas honours, including the Portuguese Order of Christ and the Order of the Rose of Brazil. He briefly considered, but did not pursue, the idea of a parliamentary career.