While it would need other photographs to be sure, I think the Bader photograpn does show one BoB-period pilot wearing a white overall of the general style which the movie depiction of AVM Park used. The visible pockets and the alignment of the front opening seem to match. It's a general sort of overall which, pre-war, could have been worn by fitters and riggers. I've a recollection of many pictures of white overalls of the same general design being worn by mechanics and drivers in motor racing, pre-war and post-war. So a garment as shown in the movie might not be strictly correct, but it might be very useful. (Not an RAF pilot, but I found a picture of Alex Henshaw in a Spitfire wearing similar overalls. He worked as a factory test pilot during the war.)