Some random thoughts:-
Ancestry's railway registers don't cover all the companies. It has some digitised railway company magazines.
Local directories usually listed station masters, but to look at them you'll have to go to
Ealing Local History Centre.
Station masters had a high status locally and he may be mentioned in a local newspaper (e.g. on retirement). The big newspaper digitisation project seems to be giving London a wide berth, so again you'll need to go to Ealing Library.
I suggest a brief e-mail to them with his name and dates and asking what they might have.They won't do any research for free, though they may do a quick lookup in a 1939 directory and solve the "which company?" question.