From the small amount of information available from DVLA, a car with this registration number still exists. As Wendax said above, it's registered as an MG M-Type from 1931, the colour is given as black, and it is on SORN (Statutory Off-Road Notification) until July 2013.
However, the date of first registration is given as 27 May 2002. It may be that this was a re-registration of the car which originally had this number - if a car has been off the road and is not on the DVLA database, but you can prove what the original registration number was, DVLA will re-allocate the same number if it is available.
But it could also be that this number was allocated to a different vehicle in 2002 as an age-related replacement for a car which had lost its original registration number.
PJ 795 was issued by Surrey County Council. Maybe Carnut could find out if it's likely that it was issued in or around 1931. If it was, then it's feasible that it could originally have been on an M-Type, and that could therefore be what the puzzle car is based on. If it falls outside the 1929 to 1932 bracket, then it could originally have been on something else, and only transferred to the M-Type that currently has it in 2002.