Barlow is the son of Andrew Dalmahoy Barlow (1916–2006) and his wife Yvonne. He is thus the grandson of
Alan Barlow, and his wife
Nora (née Darwin), through whom he is a great-great-grandson of
Charles Darwin. He is the nephew of
Horace Barlow (also FRS and Fellow of Trinity). In 1994 he married Colleen McLaughlin. Barlow worked as a research fellow of the
University of Liverpool 1978–1980. He was a Fellow of
Trinity College, Cambridge, 1979–1992. He worked in the
Statistical Laboratory, University of Cambridge 1981–1985 and was a Royal Society University Research Fellow 1985–1992. ==Work==