I've rebuilt quite a few old utility bikes over the years. This includes mainly English and American single and three speed bikes dating from the 1930s-1970s. I've seen a number of people struggle when building their own projects over what kind of tires they need. Here are my notes below:
"26 x 1 3/8" (English): when you see this nominal designation on an English bicycles, you want tires with a 590mm bead. The new, replacement tire should say something like "590-37" on the side wall. This is a very common size of tire, still made today. It's the familiar size of the Raleigh Sports and similar English "light roadsters". The other tires listed below will not fit this rim size because they are too big. Fortunately, this is the easiest tire size to find I am going to describe,.
"26 x 1 3/8 (Schwinn S-6) aka 26 x 1 1/4 (English): this tire has a 597mm bead seat. The 590mm tire (described above) will very likely not fit on the rims for the Schwinn S5/S6 tire. In England, this size is also known as 26 x 1/4, but it's the same 597mm tire that Schwinn called 26 x 1 3/8. There are a couple of tire models in this size made today, but not as many as the 590mm size described above.
"26 x 1.375" (American): this is totally different from 26 x 1 3/8, despite the fact that it would seem at first as if they are the same thing. In fact, the 26 x 1.375 tire has a bead of 599mm and will not interchange with the 1 3/8 English pattern tire. Do not attempt to fit the English size 1 3/8 (590mm) tire onto a rim that wants 1.375 tires. These tires were made until some time in the 1960s, as far as I have seen. Most of these tires, I see, are cotton chord tires from the 1940s. I've seen a few nylons from the '50s-60s era, but nothing newer.
A common question:
"I have a really old U.S.-made lightweight from the 1940s, where do I get 26 x 1.375 replacement tires?"
These 599mm tires are no longer made, and probably have not been made in any real numbers in 50+ years. That's the bad news. The good news is that the 597mm size (the Schwinn S-6 size listed above) may fit your rims. The 2mm difference is very small. If you have rims with relatively short sidewalls, as were made by Lobdell, or those which were often on the Westfield/Columbia, Dayton, and CWC bikes, there's a good chance you can buy a set of Schwinn S-6 (26 x 1 3/8 Schwinn, with the 597mm designation on the sidewall of the new tire) and work them onto the rim by hand. In fact, I found the fit on Lobdell and Westfield/Columbia rims to be very good and not all that difficult to do by hand, without the help of tire levers to mount.
Again, you cannot use the English 26 x 1 3/8 (590mm) tires on your 26 x 1.375 rims. The English tire is too small. But do look into the Schwinn sized tires for your bike - you may find new tires at a reasonable cost.
If you really must have original 26 x 1.375 tires for a museum piece or the like, try eBay or the The Classic and Antique Bicycle Exchange (www.thecabe.com). Be prepared to pay a lot more for good, original tires than a new set of the 597mm (Schwinn S-6 26 x 1 3/8) tires would cost. For riding, I urge you to try the Schwinn tires - at least buy one and see if you can fit it to your rims.