She joined GLR in London, as a junior reporter and went on to present the Breakfast Show with Gideon Coe three years later, winning a silver Sony Award in 1995.

[18] In 2004, Glover took over from Eddie Mair as host of Sunday morning news analysis programme Broadcasting House, winning a Silver Sony Award in the same year.

[27] In Autumn 2015, she launched My Perfect Country on the BBC World Service, a current affairs show made in partnership with the UCL Institute for Global Prosperity.

It puts two different groups of people in separate rooms to discuss the same topic e.g. Brexit or immigration and then brings them together to see if they have changed their positions.

[29] On 29 March 2017, Glover, together with broadcaster Jane Garvey started a weekly podcast series on BBC Radio 4, Fortunately: A frank look behind the scenes with broadcasters Jane Garvey and Fi Glover as guests from Radio, TV and podcasting share stories they probably shouldn't.

[14] Guests on the show include Ian Wright, Anne Tyler, Monty Don, Ruth Jones, Will Young, Sara Cox, Claudia Winkleman, Miriam Margolyes, Will Self, Jeremy Vine, Ken Bruce, Tracey Thorn, Emily Maitlis, and Kirsty Wark.

[31] In April 2017, Glover launched a new BBC Radio Four series, Glass Half Full, chairing debates between optimists and pessimists on key issues such as health care, population growth and gender equality.

[36] In September 2022, it was announced that Glover would join Times Radio to host a daily, two-hour show with Jane Garvey.

[42] Glover was the Chair of the Orange Prize for Fiction in 2009[43] and is a Founder of Sound Women, a lobby group set up to campaign for parity in the broadcasting industry.

[9][44] Glover is also the patron of Adfam, a national charity working to improve life for families affected by drugs or alcohol.

[7] Glover was born in Slough, Berkshire,[46] but grew up in Hampshire, with her mother Priscilla (Cilla) and sister Isabella (Izi), while her father was in Hong Kong establishing a business.

Her mother's father was Chassar Moir, an obstetrics professor credited with saving the lives of countless women worldwide.