Tire sizes don't really reflect reality, but I think if you put a 28" rim with a inflated tire on it beside a 27" rim with a inflated tire the 28" would look a bit bigger cause the tire is actually a lot larger.

A english british roadster 28" tire is bigger than our old Canadian 28" tire (which is the same rim diameter as 700c as mentioned).. I have no idea what the size of the American 28" tires are.. didnt they go extinct in the 20s or 30s when balloon tires came out?

As for the original poster I suggest you just chuck those 700c wheels on and see if you can get the brake pads to match up with the rim sidewalls, if they line up you're in.