Following the Oxburgh review of Earth Science departments, Baker returned to Leeds.
His work began with Mount Misery volcano on the West Indian island of Saint Kitts; continuing with the volcanoes on the islands of Saint Vincent, Montserrat and Saba, Lesser Antilles.
When the volcano Tristan da Cunha, in the South Atlantic, erupted in 1961, Baker joined a Royal Society expedition led by Ian G. Gass to investigate.
Baker worked there and at Deception Island, off the Antarctic Peninsula, as it had a series of volcanic eruptions (1968–70).
Baker worked on Ojos del Salado, on the Argentina–Chile border, the highest active volcano in the world.