Phillips began his career doing postdoctoral research at the University of Texas at Austin and the Academy of Sciences of the USSR. He was appointed a lecturer in chemistry at the University of Southampton, rising to the status of Reader then becoming Wolfson Professor of Natural Philosophy, at the Royal Institution. In 1981, Phillips became a founding member of the World Cultural Council. In 1989 he moved to Imperial College, London as professor of physical chemistry and held a number of senior posts there.
In 1987 he gave the Royal Institution Christmas Lectures on television. He was appointed Officer of the Order of the British Empire (OBE) in 1999 and Commander of the Order of the British Empire (CBE) in the 2012 New Year Honours for services to chemistry. In May 2011 he was the guest on Desert Island Discs and in June 2012 was Michael Berkeley's guest on Private Passions.