In virtually any civilian organisation, an executive of status equivalent to a Wg Cdr / Lt Col / Cdr would be entitled to a company car, and a nice one to boot.
Though in many companies it's now paid as a car allowance, with a requirement for a minimum age/size/standard.
It could make more sense for MoD to contract with a car hire operator to provide a rental fleet on the base, which can be booked and used for official and private use, at contract rate for official bookings. The hire charge then comes from that squadron/unit's transport budget, just like air/rail travel. My guess is that such a budget does not exist at that level, though, but that's how it would be on Civvy Strasse.