Kenda cyclo cross 27 x 1 3/8 fit on 27 x 1 1/4 rim?
You can confirm tyre fit using the ETRTO spec, which should be specified on the sidewalls of your Kendas and the tyres that were previously fitted.

the format is

ww-ddd


where ww is the nominal tyre width (often measured at the widest point when fitted to the manufacturer's test rim, rather than at the tread) in millimetres, and ddd is the bead diameter in .

I would expect a 27 x 1 1/4" tyre to be specified 28-630.

According to Sheldon, there is no other standard bead diameter using 27" as its nominal measurement, so any "27" tyre is likely to have a 630mm bead. 1 3/8" is equivalent to 35mm.

I have not previously encountered any cyclists using 27" wheels for cyclocross. I assumed "700c"/622mm to be panacea for all but the shortest of CX competitors.