"True" 28 inch wheels measure 635mm at the bead-seat. 700c wheels measure 622mm at the bead-seat. Regardless of how idiotic folks are now and were BITD, the fact is, Canadians and Northern Europeans called fatter 622 rims "28inch" since pre-WW2. In America, BITD, 28" meant 635, and that's how the Brits, the Indians, and much of Europe kept it for a very long time... But these days, we're seeing 28" labels on more and more 622/700c rubber, probably b/c the 635 size is getting ever-closer to obsolete...
But, it ain't obsolete just yet. You can buy modern 635 rubber in the classic 28x1-1/2" size for cheap. Get yerself some Delta Cruisers, by Schwalbe. They come in black, cream, or magenta (!)... you can get'm with a reflective stripe, but something tells me that you'll opt for the plain versions, which start at about $19. (Magenta only come with the reflective stripe, and cost $27, but I'm guessing you won't go that route....) Current-production 635mm rims can be purchased, typically with a "Westwood" profile for rod brakes, and most often in cheap chromed steel iterations. You can find 635s in black painted steel or alloy versions, but typically only thru European/Asian vendors. Pay close attention to the spoke-hole count; most 635s were most often used on Brit Roadsters and their Indian & Chinese clones, so they will often have a 32h front/ 40h rear set-up. Yellow Jersey in Wisconsin has some, including 36h, chromed steel, probably made in India.....
http://www.yellowjersey.org/eastbits.html
But yeah, you can run 700c tires on that frame, too. Measure between the stays (chain- and seat-stays) about 320mm (which is 12-5/8" in 'Murrkin) from where the axle will be, to see how fat you can go. They offer 622 rubber in widths from 19mm up to 3"... I bet you could squeeze some 622x48mm (1.9") tires in there, but maybe not if you're running fenders. But, that's just me, some slob making guesses on the internet. Only real measurements will give you the truth, and the truth will set you free.
(Or, play it like a rill pimp and run actual 28" wheels/rubber. That's what you're Elgin was made for, right? But that's just the same slob, offering up his opinion....)
HTH
-Rob
