Alice, not her real name, was just 16 when she claims she had a three-month relationship with Brand.
At the time, in 2006, he had a high-profile show on BBC Radio 6 Music. He was aged 30.
Now in her 30s herself, the woman set out her allegations in an interview with Radio 4 Woman’s Hour.
On one occasion, she claimed that she was at Brand’s home when he told her that the BBC car was at her disposal.
“He had a friend who was taking him to do his radio show so he said to me: ‘Oh, you get in the car and you go wherever you need to.’
“So I took the BBC car that time. And on another occasion it picked me up from school,” said Alice.
She claimed that Brand also had an account with Addison Lee, the taxi company, but that she used BBC cars on more than one occasion.
“He had two car accounts – we weren’t Uber-ing then,” she said.
“He had an Addison Lee car account and then … the BBC would arrange cars for him.
“I’d seen him previously being picked up from his house by BBC cars so I knew the difference. It was a chauffeur-driven car, it was different from just calling a cab.”
Alice demanded to know why the BBC had not kept a closer eye on Brand, given his reputation.
“He had a very well-known record of doing things that were inappropriate on the air, having inappropriate confessions,” she said.
“I don’t think he was being held to the same standards [as] other presenters [or] anybody else that was working at the BBC.
“There were exceptions and allowances made for him and we need to ask ourselves why.”
Brand denies all allegations against him. The BBC said it was investigating “as a matter of urgency” the issues raised.
In a previous interview with The Sunday Times, Alice said another taxi driver had begged her not to go inside the house after realising that it belonged to Brand, saying he had a daughter of her age.
She claimed that the driver said: “You could be my little girl, and I would want someone to do this for her.” He offered to take her home without charge, but she declined.
In that interview, Alice alleged that Brand – who she said referred to her as “the child” – sexually assaulted her in his home, and only stopped when she punched him in the stomach.
They met, she claimed, when Brand approached her in Leicester Square after she had been shopping.
He rifled through her bags, pulled out one dress and said: “You’re going to wear this on our date this week.”
Alice told Woman’s Hour that she confirmed her age to Brand in a subsequent phone call, before their date took place.
She said that her mother was horrified to learn that she was in a relationship with Brand and had done all she could to stop it.
“She followed all those motherly impulses: she took my phone away, she’d try to keep me confined to the house,” said Alice.
“But I’m 16 years old, so she can’t do that indefinitely. I need to go to school, I need to go to after-school activities, I need to see my friends. And it was within those times that I would snake off and see him.”
She alleged: “Russell groomed me and told me to save his number in my phone under a different name so that nothing was flagged when there were messages coming up.
“He coached me on what to say to my parents and there was nothing she could do to protect me from being in that relationship.”
Alice said her mother had “breakdowns” about the relationship. “People say: ‘Well, just call the police.’ And then what? I was legal.”
Alice called for a debate on the age of consent to prevent teenagers being exploited by adults.
She also claimed that Brand’s management at the time knew that he was in a relationship with a 16-year-old but urged him to hide it for the sake of his career.
John Noel Management, which represented Brand from 2002 to 2017, told The Times that for legal reasons it was not in a position to respond to questions.
In a YouTube video on Friday night, Brand described the claims about him as “a litany of extremely egregious and aggressive attacks”.
He said he “absolutely refutes” the allegations and that his sexual relationships were always consensual.