Okay, after marking out my hole positions yesterday, today I got down to drilling.
Bridge Studs
Vernier calipers on the bridge stud collars showed that I needed a 11.5mm diameter drill bit. After carefully lining everything up on the pillar drill and setting the correct depth I drilled the holes. Success, everything lined up nicely! Next I drilled the holes for the volume and tone knobs, all the way through so that I could set out the control cavity on the back of the guitar.

Machine Heads
I carefully laid out the machine heads to find the correct positions, to make sure the machine head bodies didn't clash and that they didn't fall of the edge of the headstock. Using the vernier again, I used an 8mm bit and started drilling.
Once I'd drilled the holes, I did another quick check to make sure all was well - phew, no problems!
I drilled these holes all the way through so that if any wood broke out the back during drilling it would get lost when I cut the rear of the headstock away to make it the correct thickness, which is my next task...