But the prince, who strenuously denies the allegations, was instead swamped by criticism that has focused on the property he has lived in effectively rent-free since 2003.
The ability of MPs to discuss matters relating to the royal family is constrained under the Commons’ procedures.
The guide to the rules, known as Erskine May, states that “unless the discussion is based upon a substantive motion, drawn in proper terms, reflections must not be cast in debate upon the conduct of the sovereign, the heir to the throne, or other members of the royal family”.
With the Government unwilling to table a motion to discuss Andrew due to the wishes of the royal family, an opposition day debate could be a way for MPs to speak out.
A Liberal Democrat source said: “We need to explore all options, including an opposition day debate, to ensure Parliament can scrutinise this properly, from Prince Andrew’s residence at Royal Lodge to his dukedom.
“The first thing we need is proper transparency and accountability – that’s why we have called for the Crown Estate and Prince Andrew to give evidence under oath in Parliament.”
The Lib Dems have one opposition day left this parliamentary session, but no date has yet been allocated for it.
The source told the PA news agency: “We’ll take a decision on what is most important for the national interest as and when the government tells us when it will be.”
The Lib Dem insider indicated that they hoped the King would be willing to take action.
“It’s right that we’re led by the King on this, and if Parliament does have to act we hope it can be be hand-in-hand with the Palace,” the source said.
Although Andrew has given up using his Duke of York title, only a law passed by Parliament can formally remove it.