For comparison purposes, you might want to take a look at this thread about a track bike that -holiday76 dug up a few years ago. I'm almost finished restoring that one now; it turned out to be an "Alvin" from the "Velox Cycle Company" (i.e. New York builder Alvin Drysdale). The serial number, which is stamped under the BB and on the back of the fork crown, points to a 1936 date. So obviously a later bike than yours; but it resembles yours in a lot of details: bolted seat stays, mashed front dropouts, crude lugs, etc. The Alvin was the bottom of Drysdale's line at the time; the high end bikes were really quite lovely.

The lugs, BB shell, fork crown, and presumably tubing on the Alvin were all British. BB shell and BB bearings were all made by Walton and Brown. The words "British Made" were stamped on the left side of all the lugs and on the outside of both rear fork ends.

I am guessing yours, since it has a cottered crank and lugged construction, came from a small maker who like Drysdale used English components.