Wicks was born Beverly Victoria Anne Wicks in Chippenham, Wiltshire, England, to Brian and Judith Wicks. Wicks's mother, Judith Bates, born 1933, was the second child of the Writer H.E. Bates. Wicks is the niece of Jonathan Bates, the award-winning Sound Editor who died in 2008, and the television Producer, Richard Bates, who produced the television adaptation of The Darling Buds of May. Wicks is a Director of Evensford Productions Ltd, the company set up in 1955 to protect and promote H.E. Bates's work.

In 1984 Wicks married Peter Williams (divorced 2004); they have one daughter, Madelaine Rose, born 1985.

Her first job was as Acting Assistant Stage Manager at Northampton Rep for a year, before going to Bristol Old Vic, Regent's Park and then the RSC. In 1986 Wicks was in Andy Hamilton's black comedy Tickets for the Titanic, and then went on to play Sally Smedley in all six series of Drop the Dead Donkey. The Mighty Boosh, is an award-winning radio, television and stage show created by Noel Fielding and Julian Barratt. Mrs Gideon was the Head of Reptiles at the Zooniverse in Series 1. Wicks also played Harriet Lawes, the Head of College in series 1, 2 and 3 of Skins.

Wicks joined the 'Wrestling School' in 1996. The company was formed in 1988 for the sole purpose of performing the work of the dramatist Howard Barker. Since joining the company Wicks has appeared in 9 plays by Barker, performing in London, Berlin, Stockholm, Copenhagen, Adelaide and also in Rouen, Grenoble, Le Mans and Paris for the co-production of Les Animaux en Paradis, which was performed in French by 4 British and 5 French actors. Wicks is an Associate of the Wrestling School. In 2010 Wicks was invited to the Segal Theatre Center in New York as guest of Theatre Minima to celebrate a day-long event on the work of Howard Barker.

Wicks played the hgh priestess of the Sybillines in The Fires of Pompeii, a 2008 episode of Doctor Who. In 2014, she played Dorothy Clarke in The Imitation Game, and Susannah Marshall in the E4 drama Glue (2014).