i have an old super elliott track frame from the 60s or so with a BSA headset. the headset is unusual in that it consists of races that simply sit in the two ends of the head tube, which are flared to accommodate them. it also has a top race and a locknut. the fork, however, appears to be a later replacement, and has no crown race to mate with the bottom head tube race. any idea of a source for such a part for old headsets like this? i think they were relatively common among british and australian bikes of the day. i'm told that they take either 1/8" or 5/32" ball bearings.

below is a picture of the head tube. you can see the flares of the head tube and one of the races sticking out partway on the top, underneath the top race. let me know if additional pictures would help.

also, here's a link to a recent ebay super elliott auction. i think this is an older frame than mine, but it has the original fork and the headset design looks similar.
https://cgi.ebay.com/Super-Elliot-vin...QQcmdZViewItem

This is only a guess, but is this type of headset called a continental headset? I'd be looking through the crown races that might have been 'collected' in an older bikeshop. You might be lucky enough to find a crown race to match your half. As for the balls - I would try both sizes in the top race and see which size fits. Loose balls can't cost that much.

Take it to a bike shop that handles quality BMX bike and parts---the new BMX headsets are somewhat like it---you might get luck and get a fit---worth a try---sam

i've found this type of headset (well almost.. the races sat loose inside flared cups that were pressed into the frame conventionally) on a common and lowly phillips 3-speed from 1955..
so perhaps more common and even later 3-speed parts would be a good starting point for searching replacements