Garvey became 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, Jane was presenter of The Breakfast Show at BBC Hereford and Worcester, where Ben Cooper (now head of daytime programmes at Radio 1) worked as her assistant.
Garvey was the first voice on Radio Five Live when it launched at 5am on 28 March, 1994. She became the co-presenter of Radio Five Live's award-winning breakfast programme in 1994, and also presented the Everywoman programme on the BBC World Service. 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 September 2007, it was announced that she was to be leaving the Five Live after 13 years.
From Monday 8th October 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.