Born Beverley Jane Moxon in Morley, West Riding of Yorkshire to Clive and Mavis Moxon. Clive was a baker and Mavis was a concert pianist. She has a younger sister called Stephanie.
She attended Elmfield and Peel Street schools in Morley, and also Bruntcliffe High School in Morley. At the age of seven, Beverley made her acting debut as Darius the page boy. After leaving school in 1973, she took a job as a shorthand typist. She later turned to acting and appeared on stage as Jaqui Coryton in Noël Coward's Hay Fever, Liz and Rita in Billy Liar and The Wicked Queen in Snow White.
Beverley is known for her roles as June Dewhurst in Coronation Street, but she returned to the series in the new and more significant role of Liz McDonald in 1989 and Flo Henshaw on BBC Three's Two Pints of Lager and a Packet of Crisps.