[3] From 1993 to 1998, Conway was educated at The Oratory School,[4] a Roman Catholic boarding independent school for boys in the village of Woodcote in Oxfordshire, followed by Pembroke College, Oxford, where he took an MA in English, and after having worked for several years, gained a Fulbright Scholarship to the Kennedy School of Government at Harvard University in the United States,[4][5] where he took an MPA (a master's degree in Public Administration).

[3] In August 2011, Conway joined Sky News as economics editor and covered topics including financial market crisis Great Recession and euro crisis.

[3][7] He is also known for his numerous stories including a G20 summit, Greek default and its rescue fund.

[8][5][9] Among his many interviewees are the managing director of the International Monetary Fund, Christine Lagarde, the Chancellor of the Exchequer, Philip Hammond, and the Bank of England Governor Mark Carney.

[10] In May 2014, he also published The Summit: The Biggest Battle of the Second World War - fought behind closed doors.