The Times has reported that Princess Alexandra, a first cousin of the late Queen, has been paying just £2,200 a year to rent a Grade II-listed home in Richmond Park.

According to the report, Alexandra holds the lease for Thatched House Lodge, a property in one of south west London's most exclusive locations.

Details of the arrangement were disclosed after the Commons Public Accounts Committee (PAC) sought clarity on Crown Estate property deals involving members of the royal family.

The scrutiny follows earlier revelations in The Times about favourable lease deals for Andrew Mountbatten-Windsor and Prince Edward.

MPs have since launched an inquiry into how effectively the Crown Estate maximises income from properties that ultimately benefit the public finances.

Alexandra, 58th in line to the throne, has lived at the Richmond Park residence since 1963.

While she has long been regarded as a hardworking but low-profile royal, questions have now been raised about how little rent she pays for a premium London property, the equivalent of just £183 a month, far below the cost of renting even a single room locally.

Princess Alexandra is a first cousin of the late Queen Elizabeth II (credit: Wikimedia Commons).

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The Times reports that the arrangement is split across two leases.

In 1971, Alexandra paid £3,000 for a 70-year lease, with rent set at £410 a year for the first 35 years, rising to £700 thereafter.

A second lease was agreed in 1995, involving a £670,000 premium for a 150-year term, with rent starting at £1,010 a year for 25 years and increasing gradually to £6,000 in the final period.

While Alexandra paid substantial upfront sums, MPs are questioning whether the premiums and rents reflect the true market value, especially as, unlike some royal leases, these agreements include no restrictions preventing her from selling them on, subject to Crown Estate approval.

The Crown Estate said agents had provided an independent valuation in line with leasehold reform legislation, and that negotiations took place at arm's length.

Buckingham Palace and the Crown Estate were approached for comment.