Minchin has worked for the Latin American section of the BBC World Service during a year in Argentina, the Today programme, Five and various local radio stations. In 2006 she toured the country in a converted bus meeting England fans as part of the World Cup coverage for BBC News.
In 2006 and 2007, Minchin was a relief presenter on BBC Breakfast while Kate Silverton covered for main anchor Sian Williams. After Williams returned, she continued to co-host the programme, and from May 2009 until April 2012 was the regular weekend presenter of the show. In December 2011 the BBC announced that Minchin would replace Williams as a main presenter of BBC Breakfast along with Bill Turnbull and Charlie Stayt when the programme moved to Salford—the first edition was presented on Tuesday 10 April 2012.