My friend Adam in England was unable to provide any information on the car ownership from the license plate, but did provide this information which perhaps will prove useful in dating the coachwork change:
The owner in the 1930s appears to have been a motor racing enthusiast (like me). The car is pictured in the car parks at Donington Park, Leicestershire ( a Grand Prix was held there in 1937) and also at Brooklands (Surrey), you can see the test hill in the background. The Brooklands picture shows the closed body, so is presumably more recent, however Brooklands closed in 1939 and never reopened after the second world war so the photos must have been taken within a year or two of each other.