Rundle, who is best known for her role as Ada Shelby in Birmingham-based gang drama, will star alongside Academy Award winning-actor Glenda Jackson in the feature-length adaptation of Emma Healey’s best-selling novel.
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Jackson will play Maud, a woman in her eighties who discovers her best friend has gone missing, but as she grapples with her worsening dementia, finds her search taking on an increasing urgency.
Rundle plays Maud’s older sister Sukey, who will appear in flashbacks. Fellow Peaky Blinders actor Sam Hazeldine, who featured in the show’s second series, will star as Tom.
The impressive cast features former Game of Thrones actors Nell Williams and Mark Stanley, while EastEnders star Maggie Steed will play Elizabeth.
Filming of the 90 minute TV film has now begun in Scotland, with the programme's transmission date still yet to be announced.
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Elizabeth is Missing has been scripted by Andrea Gibb, whose previous work includes Swallows and Amazons and several episodes of Call the Midwife.
Gibb said: “I am honoured to have been given the opportunity to adapt this beautiful story. Emma has created an extraordinary heroine in Maud – she’s funny, tenacious, loyal – while also giving us a moving portrait of dementia from the inside out.”
The BBC’s Piers Wenger added: “Part detective story, part portrait of a fracturing mind, Andrea Gibb’s witty, sensitive adaptation of Emma Healey’s novel brings this first-hand account of experiencing dementia to life.”