The report in the Times (archive link below) says that the National Audit Office recorded that 2 independent advisors had reviewed the terms of the lease at the time, so I assume things were done appropriately.
As I understand it, from discussion on another thread, the lease Andrew has is a fairly common form of long-term lease, whereby the lessee pays money up-front for maintenance/refurbishment, a very low (or peppercorn) rent, and guarantees to hand back the property in good condition at the end (which may mean further costs towards the end of the lease).
If that is the case, Keir Starmer would probably look quite foolish committing public money to an inquiry.
Archive: Times Prince Andrew lease