The pair will play Connie and Monty respectively in Richard Bean's adaptation of the 2010 film which starred Sally Hawkins.
Made in Dagenham dramatises the Ford sewing machinists strike of 1968 that aimed for equal pay for women.
Isla Blair has stage credits including A Funny Thing Happened on the Way to the Forum and The History Boys (West End), and has appeared with the Royal Shakespeare Company and at the Old Vic. Her screen credits include House of Cards: The Final Cut, Single Father and the upcoming Grantchester.
David Cardy has appeared in Ghost Stories and Dreamboats and Petticoats (West End), and has TV credits including Birds of a Feather and Trial By Jury.
Also in the Made in Dagenham cast are Sophie Stanton, Heather Craney, Sophie Isaacs, Julius D'Silva, Naana Agyei-Ampadu, Thomas Aldridge, Kate Coysten, Christopher Howell, Scott Garnham, Ian Jervis, Paul Kemble, Emma Lindars, Jo Napthine, Tracey Penn, Gemma Salter, Gareth Snook, Rachel Spurrell, Emily Squibb, Karli Vale and Rene Zagger.
Made in Dagenham, which features music from David Arnold and lyrics by Richard Thomas and is directed by Rupert Goold, premieres at the West End's Adelphi Theatre on 5 November 2014 (previews from 9 October).