I know from colleagues who work there, that CAA staff who only hold PPLs regularly fly for work trips. I believe CAA's own policy is that anybody doing this has to have an IMC rating, but that's their policy as an employer, not the law.
I've worked for several aviation employers who are quite happy about the use of private aircraft for work trips. The normal practice has been to put in an "Autoroute" printout, and claim as if you'd driven, although my current employer will also allow me to claim landing fees.
G