The whole bike looks more like a low-end BSA stock model from the later 1930s. The crankset is a swaged example with a fixed chainring that would have been considered a "utility" model. I used to own this 1951 New Hudson Silver Arrow, which was a rebadged BSA pre-war model reintroduced after BSA purchased New Hudson after the war. The one thing that distinguishes it from the inexpensive post-war models is that it still has the clip headset.
You can get bicycles like the New Hudson, in rather excellent original condition, for $300-400 if you wait for them. As someone who's collected a few of this kind I personally wouldn't take the one you've shared unless if it was a gift. Just a hunk of steel otherwise.
-Gregory
