After graduating from university, in 1967, Vereker joined the Ministry of Overseas Development, he then joined the World Bank in 1970, before going back to the Ministry of Overseas Development in 1972. Whilst at the Ministry of Overseas Development he was private secretary to Reg Prentice, Frank Judd and Judith Hart. Between 1980 and 1983 he was in the Policy Unit in the Prime Minister's Office in 10 Downing Street, working on public sector issues. In 1983 he was appointed under secretary for Asia in what was then called the Overseas Development Administration, in 1986 he was under secretary for development policy and Principal Finance Officer and he was appointed deputy secretary of the Department of Education and Science in 1988. 
In 1989 he was chairman of the Students Loans Company, in 1992 he was appointed deputy secretary in the Department of Education, in 1994 he was appointed permanent secretary of the Department for International Development, the new name for the Overseas Development Administration and finally appointed governor and commander-in-chief of Bermuda in April 2002 until October 2007. Whilst in Bermuda Tony Blair was a regular visitor to his house.
He has been a board member for the British Council, the Institute of Development Studies and the Institute of Manpower Studies and Voluntary Service Overseas, served on the advisory councils for the Centre for Global Ethics and for the British Consultancy and Construction Bureau, been an adviser to the UN secretary-general's Millennium Development Project and a member of the Volcker panel, investigating the World Bank's institutional integrity.
After leaving governmental duty he was appointed non-executive director at XL Capital Ltd. ACOBA noted "that XL does not conduct any business in the Bermuda market" and so it was "approved subject to the conditions that, for six months from his last day in post as Governor, he should not give advice on other companies there or revisit Bermuda for business purposes other than to attend Board meetings there with the approval of the Secretary of State, and that, for 12 months from that same date, he should not be personally involved in lobbying Bermuda Government Ministers or officials on behalf of the company or its clients."