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@lae
~~This size is commonly used for cycle speedway. I emailed Archie Wilkinson a while ago as my girlfriend's bike also uses Roadster wheels. They weren't listed on their website, but they do sell good quality double-walled aluminium rims in that size in silver and they've got a braking surface. If you want a singlespeed wheelset they'll probably build one up with silver rims if you ask nicely - or you could just buy the rims and build them up yourself.
Their website is:
http://www.archie-wilkinson.co.uk/wheels-and-tyres.html
Tyres can be hard to find in that size, but the el cheapo Raleigh whitewall tyres I fitted on my girlfriend's bike have actually held up fine for everyday commuting for about 18 months, and no punctures either.
Incidentally does it have rod brakes or normal calliper brakes? If it has rod brakes, then it'll need rims specifically designed for rod brakes - normal clincher rims won't work. If that's the case, then your best bet is ebay or the retrobike forums.
edit - and yeah, like Brickman says, you might consider changing to 700c. Your 26 x 1 3/8 rims are 590mm, and 700s are 622mm, so the difference isn't very big. My girlfriend's roadster takes 26 x 1 3/8 rims but since the clearances are so huge, 700cs fit too. Get some 700s designed for a hybrid with wide rims so you can fit big fat 40c tyres - skinny tyres on a roadster would just be awful. The only problem with that is that you'll certainly need new brakes - the drop on your current brakes will be too long (and rod brakes won't work on modern rims, as previously mentioned). You probably couldn't size down to 26" (559 aka mountain bike size) because you won't find brakes with long enough drop (unless you fit drum brakes... or discs... now that'd be cool), and also it'd look crap.~~
Scrap all of that - I thought you said 26 x 1 3/8, but you in fact said 26 x 1 1/4... which is pretty rare. I imagine the only rims you'll find are NOS ones - but the good news is that they're 597mm, which is only very slightly smaller than 700c (622mm). You shouldn't have any problems changing to 700c rims as these old bikes have massive clearances. Just make sure you get wide touring/commuting type rims so you can fit some decently wide tyres.