This was a bit of a mystery. In the negative index the only A.W. Croughton Sentinel is LNER Sentinel RC No 51909 at an unknown location in 1936. However the number on the side is partially readable and definately includes a '3'. The platform seatback name ends in xxtion and the telegraph post in the distance matches one at Thornton Junction exactly. Furthermore No 313 'Banks of Don' was based at Thornton Junction for working the Methil branch from 1931 to 1944, for some of this period it had cranks and outside coupling rods on the power bogie.
There is another photo published in 'The Weymss and Buckhaven Railway' that shows 313 in an identical condition (including the bent item on the roof) so I am convinced this is indeed that railcar.

Photo: A.W. Croughton / Rail Archive Stephenson