Jess is a financially struggling single mother living in a declining coastal town. She juggles multiple low-wage jobs, including cleaning holiday homes and bartending at The Feathers pub, to support her daughter and stepson. Despite her precarious financial situation and mounting overdue bills, she maintains a determined optimism and fiercely protects her family.

Ed is a 34-year-old tech millionaire and software developer who recently sold half of his company. He faces suspension and criminal charges after a former girlfriend uses a stock tip he provided to make illegal profits. Isolated and accustomed to using his wealth to avoid personal problems, he retreats to his sterile seaside holiday home to hide from the fallout.

Tanzie is Jess's 10-year-old daughter and a true mathematics prodigy. She finds deep comfort in the logical, orderly world of numbers, which sharply contrasts with the unpredictable nature of her family's finances. She is socially naive, highly literal, and frequently targeted by bullies for her unfashionable clothing.

Nicky is Jess's 16-year-old stepson. He wears heavy goth fashion, including dyed black hair and eyeliner, to construct a defense mechanism against his feelings of parental abandonment. His appearance makes him a frequent target for physical violence and harassment in their small town. Isolated and cynical, he spends much of his time communicating with people in online gaming communities.

The Fishers are a local family living in the Thomas family's neighborhood who act as a collective antagonist. Led by the mother, Leanne, and her violent son, Jason, they relentlessly bully Nicky for his goth appearance. They represent the hostility, prejudice, and physical danger the Thomas family faces in their daily lives.

Marty is Jess's estranged husband and the biological father of Nicky and Tanzie. He left his family nearly a year prior, claiming severe depression, and asserts that he moved in with his mother in Scotland. He avoids all financial responsibility for his children and relies on excuses to maintain his distance.

Norman is the Thomas family's oversized, flatulent rescue dog. He is a constant, chaotic presence in their daily lives, requiring special accommodation on their travels due to his massive size and smell. Despite his physical imperfections and messiness, he is deeply loved.

Nathalie is Jess's best friend and partner in their struggling cleaning business. Pragmatic and somewhat cynical, she frequently questions Jess's optimistic plans, particularly her goal of sending Tanzie to an expensive private school. She provides a realistic perspective on their working-class constraints.

Deanna is a former university acquaintance of Ed Nicholls. Following his divorce, they enter a brief affair. Struggling with significant debt, she accepts money and a stock tip from Ed, which her family uses for illegal insider trading, triggering a criminal investigation into Ed's firm.

Ronan is Ed's long-time business partner and the co-founder of their software company. When Ed is suspended for alleged insider trading, Ronan quickly distances himself, feeling entirely betrayed by the scandal that threatens their newly launched product.

Gemma is Ed's sister. She continually pressures him to visit their terminally ill father in the hospital. Unaware of the true extent of Ed's legal troubles, she interprets his absence as typical self-absorption and emotional detachment.

Mr. Tsvangarai is Tanzie's dedicated math teacher. He recognizes her extraordinary potential and encourages her to apply for a scholarship at St. Anne's. He also informs the Thomas family about the Math Olympiad in Scotland.

Bob is Ed and Gemma's father. He is frail, terminally ill, and confined to a hospital bed. Despite Ed's prolonged absence, Bob holds out hope that his son will eventually visit him.

Anne is Ed's mother. She spends her days living out of hospital waiting rooms as she cares for her dying husband, Bob. She carries the emotional weight of his illness while managing her children's strained dynamic.

Linzie is a woman living in a highly affluent Scottish neighborhood. Her tidy, comfortable life in an executive home stands in sharp contrast to the constant financial struggles faced by the Thomas family.

Paul is Ed's lawyer, tasked with managing the heavy legal fallout from the insider trading investigation. He provides Ed with bleak updates regarding the police's progress and the mounting evidence against him.

Liam is a local taxi driver and a casual friend of Jess. He assists her by safely driving a heavily intoxicated Ed home from the bar, an event that inadvertently sets off a major chain of events regarding Ed's dropped cash.

Lara is an Italian actress and Ed's ex-wife. After securing half of his fortune in their divorce, she continues to contact him to request additional money, adding significantly to his financial and emotional stress.

Sidney is a finance director from the parent company that recently acquired half of Ed's software firm. He represents strict corporate authority and is responsible for suspending Ed when the insider trading allegations surface.

Jez is Ed's hacker friend. He assists Ed in remotely accessing the Facebook account of Nicky's primary bully to post embarrassing messages and delete the anti-gay abuse targeted at the teenager.

Nigel is a neighbor to the Thomas family. When Nicky is severely beaten by local bullies, Nigel intervenes and immediately drives the injured teenager to the hospital, looking out for the vulnerable family.

Suze is Linzie's daughter. She lives in an affluent Scottish household, and her mocking behavior toward Tanzie's academic work makes Tanzie feel entirely out of place in the new environment.