Set in Europe between the First and Second World Wars, the story follows the romantic adventures of Linda Radlett, played by James, the second-oldest daughter of an upper-class family.
Emily Beecham plays her best friend and cousin Fanny Logan.
West and Dolly Wells feature as Linda’s parents, while Scott features as Lord Merlin, the Radlett’s wealthy and eccentric neighbour.
James, 32, and West, 51, prompted controversy in October last year after they were pictured together in Rome during filming for the drama.
Married West then flew home and posed for pictures with his wife Catherine FitzGerald, 49, outside their house in the Cotswolds.
The Wests later said their marriage is “strong” and they are “very much still together”.
Mary Poppins Returns star Mortimer stars as Fanny’s mother, John Heffernan as Davey, Annabel Mullion as Aunt Emily and Beattie Edmondson as Louisa Radlett.
The Pursuit Of Love is produced by Open Book and Moonage Pictures for the BBC and is a co-production with Amazon Studios in the US, Canada, Australia and New Zealand.
It airs on BBC One and BBC iPlayer on May 9 at 9pm. All three episodes will then be available to watch as a boxset on BBC iPlayer.