Grubb was born in Dumfries, Dumfriesshire, but moved to Ealing West London when he was a small child.
His father William Grubb was a research chemist at the Imperial Chemical Industries and later worked as a science teacher in London.
For this work he received a special mention as runner-up for the Thomas Henry Huxley Award of the Zoological Society of London in 1968.
He published checklists of West African mammals (for instance for Sierra Leone, Gambia, and Ghana) and wrote several revisions, including on warthogs, gerenuks and buffalo.
In 1993 he co-edited the IUCN publication Pigs, Peccaries, and Hippos: Status Survey and Conservation Action Plan.