Born in Windsor, Berkshire, England, Alcock attended Westlake Boys High School in the North Shore of Auckland from 1965 to 1968.

He began his career as long-term member at the Institute for Advanced Study in Princeton, New Jersey (1977–1981).

His primary research interests are massive compact halo objects, comets and asteroids.

[1] Both awards recognized his pioneering work as principal investigator on the major U.S. project to search for massive compact halo objects and estimate their contribution to the dark matter component of the Milky Way's galactic halo.

As director, he oversaw an annual federal budget of $111 million, and a staff of approximately 540 Smithsonian employees (as well as visitors, fellows and students) and 130 Harvard faculty, employees, visiting scientists and graduate students.