Grubb was born in Ealing, West London. His father William Grubb was research chemist at the Imperial Chemical Industries and later worked as science teacher in Scotland. His mother Anne Sirutis was a school teacher from Lithuania. His younter sister Katrina is an artist. After his BSc graduation in Zoology at the University College London Grubb was research assistant in the Wellcome Institute of the Zoological Society of London. In the early 1960s he went to St Kilda, Scotland for three years where he studied Soay sheeps for his PhD thesis. For this work he received the Thomas Henry Huxley Award of the Zoological Society of London in 1968. In the same year he took part at the Royal Society expedition to Aldabra where he worked particularly on the Giant tortoises. Subsequently he lectured on the University of Ghana for twelve years. Furthermore his main research field was the taxonomy and distribution of African mammals.