Thank you everyone
bkay: I thought that was the correct path, I misunderstood the question about the horizontal bar to be about the tension guide.
Macybaby: the plate does indeed say 15J, and since this is a treadle, I am going to assume it is a 15-88...
As best as I can determine from following the links and guessing at the rest, I'm thinking that given the relatively low serial number, this machine was made in 1954 at the St John factory. But of course I may be wrong, it wouldn't be the first time