The 37-year-old daughter of the former England footballer Paul Gascoigne said she had not spoken out before because of "embarrassment and shame". More than 200 women have come forward to lawyers with allegations relating to Fayed since a BBC documentary on the businessman was broadcast last month.
The Met police have said that 21 women approached the force before the BBC film and that 60 more women have contacted them since.
According to Harrods, the luxury store in Knightsbridge owned by Fayed until 2010, more than 250 people are part of its process to settle compensation claims.
Gascoigne, who is a model and reality TV star, said she had got to know Fayed through her parents, Paul and Sheryl. She said: "He used to tell me how much of a bad father my dad was, because he used to come into the store drunk.
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