In response, Nandy called for a “full and urgent explanation” of how the “incredibly serious allegations” about Sullivan had been handled.
She had meetings with West Ham and the FA on Wednesday to seek answers on its response to the safeguarding concerns.
West Ham is understood to have made clear it was confident in its “robust safeguarding measures”.
Meanwhile, it has emerged Boyle Sports, one of West Ham’s main sponsors, had not been made aware of the restrictions placed on Sullivan.
In a statement, Boyle Sports said it was “extremely concerned at the serious nature of the allegations levelled against David Sullivan”.
“It is our understanding that the Independent Football Regulator is reviewing this matter urgently and we wholeheartedly support their efforts in doing so,” the statement added.
The BBC and Times investigation also revealed that eight women, including one who was part of the investigation, have gone to the police with disclosures about Sullivan’s conduct. None of those cases have resulted in charges.
Sullivan, 77, held the joint chairman position at West Ham for 16 years, and was the club’s largest single shareholder following the death of his business partner, David Gold, in January 2023.
He resigned as joint chair on Saturday, saying he wanted to focus on fighting what he called “factually incorrect and entirely false, decades-old allegations concerning my personal life”.
In his resignation statement, Sullivan said that “after a lifetime spent building businesses in the adult industry in which I have met thousands of women, it is sadly inevitable that a small number of improper conduct claims are being made against me”.
West Ham and the FA have previously said they have clear and robust safeguarding measures in place, and were unable to comment on individual cases.