The decision by the public accounts committee to investigate the terms under which members of the royal family occupy properties owned by the public body that is the Crown Estate will have caused dismay and concern within the Palace.

What began as public outrage about Andrew Mountbatten-Windsor paying only a peppercorn rent to live in the 30-room Royal Lodge has widened into the much broader issue.

The Palace has been desperate to ringfence Andrew as an isolated problem, but it is now clear that he is merely the extreme manifestation of a wider culture of questionable royal entitlement.

MPs will doubtless look into Royal Lodge in detail. One unresolved question is the cost of works to deal with the dilapidation of the property. Andrew in theory is entitled to a refund of £488,000 from the surrender of his 75-year lease and if the remedial works cost less than that, he will receive money back, an outcome that would cause a public storm. A figure for the works in excess of £488,000, as seems likely, will generate a bill for Andrew which he will not want to pay.

When MPs pulled at the loose end that was Andrew, the royal ball of string began quickly to unravel.

We have already learnt that Edward and Sophie are also on a peppercorn rent, and this for Bagshot Park, a 120-room mansion sitting within 51 acres. And that Princess Alexandra — who’s she, you might ask — is able to enjoy Thatched House Lodge in Richmond Park for a rent of just £225 a month, about a fifth of what a struggling couple would pay for a one-bedroom flat in Romford.

In Edward’s case, he paid a one-off sum of £5 million back in 2007 for his “forever” property. That equates to just over £250,000 a year even if he were to vacate the property tomorrow, and the equivalent of less each year the longer he stays.

However, £250,000 a year is a long way behind the market rent for this property. There was in 2007 a serious bid to turn Bagshot Park into a conference centre, which would have generated a much higher rent, but the Crown Estate leased it to Edward instead. We need to know why.

This is not mere idle curiosity. The income from the public Crown Estate goes to the Treasury, so a failure to maximise the rental income from its vast property portfolio represents less money for the public purse, and so an indirect public subsidy to rich members of the royal family.

Pulling at the ball of string will also lead to questions about the 52 grace-and-favour residences I discovered the King has at his disposal from the Crown Estate. I asked for a list of these and whether market rents were being charged. The Crown Estate refused to give me that information. Perhaps the parliamentary committee will have better luck.

The Palace also refused to tell me how many grace-and-favour residences the King controls in total. The most up-to-date figure I could find was 272, and that was in 1993.

The committee also needs to look into the property portfolio of the royals more generally. There are now 11 working royals, eight of whom are couples: Charles and Camilla, William and Kate, Edward and Sophie, and the Duke and Duchess of Gloucester. That would imply a need for seven residences, with, being generous, an additional country retreat for the first two pairs mentioned above, so nine in total. Yet between them, they have access to around four times as many properties. Self-evidently, most of these properties will sit empty most of the time, some semi-permanently it seems.

Earlier this week, before the public accounts committee announced its inquiry, I wrote to the chairman, Sir Geoffrey Clifton-Brown, urging a much wider inquiry into royal finances. This is a key time with a review of the sovereign grant due next year.

The hugely unwise change from civil list to sovereign grant, made in 2011 by George Osborne, the chancellor at the time, has given a windfall of millions to the royals that would previously have gone to the Treasury, most notably from the development of offshore wind. The last year of the civil list gave the royals £7.9 million. Fourteen years later, the sovereign grant gives them £132.1 million. You do not have to be a republican to think this obscene.

Our royal family costs us about half a billion pounds a year, more than ten times that of any other European monarchy. Charles and William would be wise to drive this figure well down before parliament — and the public — does it for them.

Norman Baker is the former Lib Dem MP for Lewes and a former home office minister. He is author of And What Do You Do? What the Royal Family Don’t Want You to Know