The reach is stamped on the rear of the calipers in your photo. The Shimano 600 longer reach calipers have a stamped reach of 47-57, but a pair that I have will reach what I measure to be 59 mm. That's just enough to go from 27 inch to 700C on a Nishiki frame I have. You need to measure the distance from the axle centerline to the brake mounting hole on both front and rear of your frame, to know if 57-ish will be enough. There's a lot of variation in frames, across both manufacturers, and the decades of manufacture. Older bikes tend to require longer reach. Older English bikes, particularly, have rather long reach required for the rear wheel.

While getting a pair of longer-reach calipers may, in fact, be the cheapest solution, there are things called "drop bolts," if you can find one, that will provide greater reach (but not greater clearance if fenders are part of the build).