Journalists repeatedly asked the PM’s official spokesperson if the government – which controls the Commons timetable – would give MPs time to debate Andrew’s titles and financial affairs.
The spokesperson said: “We know that the Royal Family would not want to take time from other important issues.”
On the question of whether Andrew could be hauled before a select committee, they added: “Any decision for committees to scrutinise developments are a matter for them.”
The chairman of the influential public accounts committee, Tory MP Sir Geoffrey Clifton-Brown, has said he is writing to the Crown Estate and the government in the coming days to “seek further information on the lease arrangements for Royal Lodge”.
Earlier this week, when asked if it would launch an inquiry, a spokesperson for the committee said its programme of inquiries was “full up until the new year”.
Sir Geoffrey says the committee will make a decision next year on whether to investigate the Royal Lodge, when the Crown Estate’s next annual accounts have been published.
Prince Andrew’s ties to Epstein came under fresh scrutiny after Ms Giuffre’s memoir Nobody’s Girl revealed new details of her allegations against the pair.
Prince Andrew, who reached a financial settlement with Ms Giuffre in 2022, has always denied the allegations.
Ahead of the books publication, Prince Andrew announced he will be giving up his royal titles. Only legislation can formally remove his dukedom, which is now held in abeyance.
Calls have also intensified for Andrew to give up his Royal Lodge home in Windsor Great Park after it emerged he paid a “peppercorn rent” for more than 20 years.