Jasmine was the daughter of Disa O'Brien. Disa gave birth to Jasmine alone in a derelict building on Christmas Day 1990. She left the child in a cardboard box on Diane Butcher's doorstep. Diane and Mark Fowler named the baby Billie and looked after her until they found Disa and threatened to give the baby to Social Services unless she returns to Walford with them. Disa did, under protest, and lived in Mo Butcher's flat on the Square. With the help of Diane and Dot Cotton, Disa began to bond with her daughter and renamed her Jasmine.
Disa didn't tell anyone that her stepfather Ken Raynor was Jasmine's father. He'd been abusing her for some time, and her mother was in denial when Disa tried to tell her leading to Disa running away from home. Ken came to Walford and tricked Dot into letting him see Jasmine as he claimed to be Disa's concerned uncle and kidnapped Jasmine. Ken wanted Disa back under his control but Dot, assisted by the police, tricked him into meeting her and handed him over to the police. Jasmine was returned to Disa, and Ken was imprisoned. With the possibility that Ken could be released, Disa opened up about the sexual abuse he committed to her to her mother. Disa and her mother, Sandra Raynor, visited Ken in prison to confront him. Disgusted, Sandra informed Ken that she would be testifying in court to ensure he is imprisoned for a long time. Disa and her mother reconciled, and Disa took Jasmine back to Sunderland.