She was employed as a medical records clerk in a finance company, as a trainee for an advertising agency and as a receptionist, before becoming a promotions assistant for Radio Wyvern, where she later became news editor before leaving in 1988 to join BBC Hereford and Worcester as a reporter. The station began in February 1989. In 1989, Garvey was presenter of The Breakfast Show at BBC Hereford and Worcester, where Ben Cooper (later head of daytime programmes at Radio 1) worked as her assistant.
Garvey was the first voice on Radio Five Live when it launched at 5 am on 28 March 1994. She became the co-presenter of Radio Five Live's award-winning breakfast programme in 1994, and also presented the Everywomanprogramme on the BBC World Service. She was also the presenter of the relaunched Midday show on BBC Radio 5 Live, (during which the award-winning "Postcards from the Street" series by Stan Burridge was broadcast). Her final long-term assignment on Radio Five Live was as co-presenter of its Drive show on weekday afternoons with Peter Allen. She and Allen have won four Sony Gold Awards and their relationship on air was described in The Times in 2002 as "a marriage made in radio heaven".
In May 2007 in a discussion on the tenth anniversary of the Labour Party gaining power in the United Kingdom Garvey unwittingly revealed an apparent pro-Labour bias at the BBC. Garvey reminisced how in the morning after the general election "the corridors of Broadcasting House were strewn with empty champagne bottles - I will always remember that", though adding that the BBC had "perhaps fallen out of love with Labour" in more recent years.
In September 2007, it was announced that she would leave Five Live after 13 years and on Monday 8 October 2007 she joined BBC Radio 4's Woman's Hour programme as the second principal presenter, succeeding Martha Kearney in the role. She created a minor stir in February 2008 in a Guardian interview, describing Woman's Hour as too middle-class and fixated on cooking. She returned briefly to BBC Radio 5 Live in November 2011 as a stand-in presenter on the Double Take programme.
Garvey married the television presenter Adrian Chiles in September 1998 in Swansea. They lived in Shepherds Bush, west London and have two daughters, both born in Hammersmith and Fulham, London: Evelyn Katarina (born January 2000) and Sian Mary (born March 2003). Chiles is a well known dedicated West Bromwich Albion fan, and when asked whether West Brom would be promoted that season, Garvey commented: "I flaming hope not. Last time Albion got promoted, I gave birth nine months later."
In June 2008, Chiles and Garvey separated; they divorced in October 2009.