Dr. Alfred Jones, a British fisheries expert, is approached by Harriet Chetwode-Talbot, a consultant representing a wealthy Yemeni sheikh with a seemingly impossible dream: to bring salmon fishing to the desert. Initially dismissing the idea as ludicrous, Dr. Jones faces pressure from his superiors and the Prime Minister's office, eager for a positive story from the Middle East. Reluctantly, Dr. Jones joins Harriet and the sheikh on this ambitious project. The sheikh believes that the endeavor will enrich the lives of his people and bridge cultural divides.

As Dr. Jones and Harriet work closely together on the project, they face numerous technical and logistical challenges, forcing them to re-evaluate their personal priorities and beliefs. While Harriet deals with her own personal hardships, Dr. Jones starts to see the visionary potential of the sheikh's dream. Through their shared efforts, they begin to form a connection that transcends professional boundaries, setting the stage for unforeseen developments.