Anthony was director of the Nuffield Foundation from 1995 to 2012. He is a trustee and Vice Chair of the Bell Foundation (a new foundation with a focus on English as an Additional Language); a trustee of the Pensions Policy Institute (a pensions think tank); a member of the Education Board of City and Islington College and a member of the board of the Association of Charitable Foundations.
Continuing a lifelong involvement in the field of science and mathematics education he is a member of the Board of the Salters’ Institute, the lead charity of the Salters’ Company (a City of London livery company) and a member of the Royal Society’s Advisory Committee on Mathematics Education. He is a visiting Professor in the department of Education at King’s College, London. He was awarded the CBE in 2013, for services to education.