I just don't remember it being calculated
Indeed not ; you probably won't see anyone actually write the figures down and carry out a calculation. The CAA's computer does it automatically when any pilot's height and weight are entered . . . . . and
Can you fail a Class 1 medical on your BMI alone?
. . . . . . . yes, you can. The computer (as mentioned above) flags up a warning if the calculated BMI is in excess of a certain figure. Might be 35, or might be 38 - I'm not 100% sure right now.