This has been fun!
I have spent some hours looking thru many gap-bed lathe listings at lathes.co.uk.
Better than anything on TV!
I guess your lathe cannot be too old due the v-belt pulleys at the headstock instead of flat belt pulleys.
Any indication that the v-belt pulleys are not original?
I did NOT find an exact match.
I was hoping that this knob on yours:
would be the smoking gun....but none of the lathes had anything similar.
Does it have a hole thru it?
any indication that it is an adjustment or mount for something?
I sure do see some other similarities to a couple other lathes.......
1) the Randa:
http://www.lathes.co.uk/randa/page2.html
similarities are the tailstock and the way the apron fades off to the right side
of course there are differences too...your tailstock is offsetable, the Randa tailstock is not.
and the ends of your tailstock are straight up/down, these ones curve
tailstock:
apron:
2) the Grayson lathe has the same two similarities:
http://www.lathes.co.uk/grayson/
3) the Relm tailstock has the lock right on top like yours:
http://www.lathes.co.uk/relm/index.html
...but the tailstock shape is not right.
pe,
4) the Drummond tailstock is more similar in shape:
http://www.lathes.co.uk/drummond-flatbed-1902-1912/
and is offsetable, but the lock is not on top of the barrel...
and the headstock and beds are very different!
I might have a little more time to spend....but here's hoping someone comes along that knows it right off!
Good Luck!
-brino