Alexander is originally from Surrey and read English in the Midlands at the University of Birmingham. She initially worked for the BBC at Pebble Mill for BBC Radio 4 (where she worked on You and Yours, Checkpoint and Woman's Hour).
She then worked on BBC Midlands Today from the 1970s onwards, at one time being a main anchor. In the early 1990s she mainly presented the breakfast and lunchtime bulletins. Her regular co-presenters included Tom Coyne, Alan Towers, Sue Beardsmore and David Davies. In October 2003, the Royal Television Society presented her with a Special Award to mark thirty years in television.
Alexander was until 2012 Chairman of the Birmingham Assay Office (the first woman to hold this position). During that time she became a Freeman of the Worshipful Company of Goldsmiths and a Freeman of the City of London. She is a former Director of the Birmingham Hippodrome and a Patron of Acorns Children's Hospice, the Mary Ann Evans Hospice and cancer charity Breast Friends.
Alexander, one of the Midlands' most popular and recognisable television faces, retired after presenting her last news bulletin on BBC Midlands Today's lunchtime news on 30th October 2012, and the next evening appeared on air for the last time to receive her colleagues' congratulations.
Alexander was appointed Member of the Order of the British Empire (MBE) in the 2013 Birthday Honours for services to broadcasting and to charity in the West Midlands.