After graduating from London's Royal Academy of Dramatic Art (RADA) she worked mainly in theatre, using the received pronunciation she was taught at RADA to extend her repertoire of Shakespeare.
She also undertook television roles. The popular Lovejoy series starring Ian McShane needed a replacement when the character Eric Catchpole, Lovejoy's assistant, departed. Parish played the new assistant, Beth Taylor. Another television role was as Lola Christie, girlfriend of Mick McFarlane, the manager of the EastEnders night cafe, in 1998.
Parish has also appeared in television dramas including The Bill and its spin-off M.I.T.: Murder Investigation Team, playing DC Eva Sharpe. Before The Bill she starred in Babyfather, for which she received the Royal Television Society's best actress award in 2001 – the first black actor to win a major RTS award.
Parish returned to EastEnders in May 2006 but this time playing regular character Denise Fox. She departed from the soap opera temporarily in January 2008 in order to give birth to her daughter, returning in June 2008.
Parish appeared as Millie in the 1996 film Indian Summer (also released under the title Alive And Kicking)