Glover has been a columnist for the London Evening Standard (1992–95), The Daily Telegraph (1995–97), The Spectator (1996-2005) and The Independent (2005-12). He has written a column for the Daily Mail since 1998. In April 2012, The Guardian reported that Glover's contract with The Independent had been terminated.
In 2004, Glover proposed a new compact upmarket newspaper to be called The World with fellow journalists Francis Wheen and Frank Johnson under the chairmanship of Adam Broadbent, a former managing director of finances at Schroders plc. The proposed newspaper was loosely modeled on Le Monde in France, and was intended as a response to the dumbing down of some quality titles. It was reported that Glover and his colleagues sought only £15.4 million to launch the The World, less than the budget for The Independent almost 20 years earlier, though this amount was subsequently slightly increased. The project did not get off the ground.