Ah, no.
I hadn't realised that there were any "real" P-51 Mustangs at the Rally; there were none there when I was on the field on Saturday but there were some replicas (including the impressive Titan Mustang I mentioned).
Original P-51s are operated under a Permit to Fly, yes - but administered directly by the CAA rather than the PtF delegation that the LAA holds.
See
here, and CAP733.
As an aside, the Vulcan operates on a CAA Permit to Fly.