The weather on Storm Island is, of course, stormy. This helps establish themes of social and mental isolation, as David and Lucy live on the island and refuse to socialize or leave; David in particular becomes very bitter and isolated even from Lucy, who is confused and frightened by her husband's alienation. The storms on the island also symbolize their married relationship, and the eventual fates of both David, and Faber as he becomes involved in their lives. Lucy's life is tumultuous, as she first becomes alienated from her husband and then starts an affair with Faber, and only after the end of the book does she find a calm period in her life.
Lieutenant Commander Werner Heer looked at his watch. "Thirty minutes."
Major Wohl nodded. "What's the weather like?"
"The storm has ended," Heer said reluctantly.
(Follett, Eye of the Needle, Google Books)
Both David and Faber die during storms, which clear up as the action of the book ends. The weather also symbolizes Faber's inability to send his message to the German U-Boat; his actions are chaotic and unplanned, allowing him to be tracked more easily. Finally, by confining first David and Lucy, and then Faber, to the island, the weather causes the story's end to play out confined to a specific place, and for all the other characters to focus on it instead of on a larger landscape. This creates suspense, making the book a faster and more enjoyable read.