Look for the ETRTO/ISO size designation on the tire sidewall. A 27" x 1.25" tire should be marked something like "32-630" where the first number is the nominal width and the second is the bead seat diameter. Any tire with the same bead seat diameter (630) will mount on your rim, in principle. A particularly narrow tire may object to being mounted on a particularly wide rim, so try to get the width designation close to that of the original tire, but it doesn't have to be exact. The bead seat diameter (630), on the other hand, must match or the tire won't mount.