Initially educated at the Harrow County School for Boys, Dalgleish received a Bachelor of Medicine and Surgery degree from with an intercalated Bachelor of Science degree in Anatomy.
After various positions in the United Kingdom, Dalgleish joined the flying doctor service in Mount Isa, Queensland, then progressed through positions at various hospitals in Brisbane, Australia, before moving to the Ludwig Institute for Cancer Research in Sydney.
After completion of his training, Dalgleish returned to work in the United Kingdom in 1984 at the Institute of Cancer Research, where he helped identify CD4 as the major cellular receptor for Human Immunodeficiency Virus. In 1986, he was appointed to a consulting position at Northwick Park Hospital, in 1991 he was made Foundation Professor of Oncology at Street George"s, University of London, and in 1994 he was appointed Visiting Professor at the Institute of Cancer Research. In 1997, he founded Onyvax Limited., a privately funded biotechnology company developing cancer vaccines, where he holds a position as Research Director.
He is also a member of the medical board in Bionor Pharma. Dalgleish is a member of the United Kingdom Independence Party and stood as a 2015 general election candidate in Sutton & Cheam, finishing fourth with 10.7% of the vote.
