Oldroads.com (Menotomy Vintage) had rod brake parts for a long time on their site. I don't know if they do anymore, but it's worth a look or an email/phone call to the shop. Vin Vullo is a good guy and knows his vintage bike stuff, he might be able to help.

The Eastman parts from yellow jersey are a bit overpriced, but generally seem to fit later Raleigh DL-1 bicycles. I have a '78 and have used some of those parts successfully. Also check out their vintage brake bits page and shoot an email if need be.

What you're basically looking for are "old brake bits", which old shops or shops with vintage bikes may have sitting around in boxes or cans. Just remember to say it need not be new old stock, but just in good, working shape.

Cycles of Yesteryear (http://www.cyclesofyesteryear.com/) also may have some parts for you, though you pay through the nose for shipping from Britain. But they also may have insight in particular into very old rod brake roadsters for you.

The note about this bike being older than your average US-based DL-1 is spot-on. Most DL-1s you see here in the US date to the 60s or 70s. Stuff from before that is less common. Also beware that prior to WWII rod brake roadsters came in a variety of types and different wheel sizes, not just 28 inch. You'll want to be sure of your dimensions, then hit up the shops I mentioned (plus any others out there you can think of). That one looks pretty old compared to what you usually see here in the US. I say fix those rod brakes up and stick with the steel wheels.