Blackman, born in London the son of a doctor, studied medicine at St. Bartholomew's Hospital there, and natural sciences at Cambridge University. He remained in Cambridge for the whole of his career where he served as head of plant physiology until his retirement in 1936.

Blackman is mainly remembered for his classic 1905 paper, Optima and Limiting Factors, in which he demonstrated that where a process depends on a number of independent factors, the rate at which it can take place is limited by the rate of the slowest factor. This paper was stimulated by the research of one of his students, who showed that raising the temperature only increased the rate of photosynthesis if the level of illumination was high. Increased temperatures had no effect at low light intensities.

He had earlier, in 1895, provided convincing experimental support for the long held view that gaseous exchange between the leaves and the atmosphere takes place through the stomata, the pores on the leaf's surface.