Hi Matthew. Yes, they are within their rights. Your father-in-law took out finance for the car, and £6K is presumably the amount outstanding to settle the agreement.
In the event of the death of a borrower, the finance company becomes a creditor to the estate and is entitled to whatever the settlement figure is. A good lawyer may be able to negotiate the amount based on the size of the estate, but in principle they are entitled to whatever the amount is.