Holmes was born in London, GB. He attended St John's College, Cambridge from 1952 to 1955, obtaining a Bachelor's degree. He then moved on to the University of London, Birkbeck College where he worked on the structure of the tobacco virus. His dissertation was entitled "X-ray diffraction studies on tobacco mosaic virus and related substances." During his time at Birkbeck, he worked with Rosalind Franklin, Aaron Klug and John Desmond Bernal. In 1960 and 1961, Holmes was a Research Associate in Pathology The Children's Hospital, Boston, USA and Children's Cancer Research Foundation where he worked with Carolyn Cohen on muscle structure. In 1962, he moved to the Laboratory of Molecular Biology in Cambridge, GB and in 1968 he moved to the Max Planck Institute for Medical Research in Heidelberg, DE where he continued working on muscle physiology and established the Department of Biophysics. (In 2019, this is called the Department of Biomolecular Mechanisms.) Holmes was also the Head of the EMBL Hamburg site at DESY in Hamburg, DE from 1975 to 1976. Between 1971 and 1999, Holmes was also professor of Biophysics at the University of Heidelberg, DE.