Oh! I can actually answer this, I was a student paramedic for a while.

When you have a critical patient you radio a special frequency with your blue call request. You pass over your patient observations and pertinent details. So for example. "Patient is a 27 year old male involved in car vs pedestrian collision. Patient is GCS 3, with traumatic amputation of right foot. Obs are as follows. O2 sats 95, Heart Rate 124, BP 130/67, BM (Blood sugar) 4.3. Patient is not known to be on any medication. TNX and saline (dosages) have been administered"
(That's one that's just made up of the top of my head. I never treated anyone with an injury like that thankfully)

Then control will tell you to go to the nearest appropriate resus unit. And blue lights mode is engaged. You make the request so that staff at the hospital are ready and waiting for you. In my example a surgeon would be probably be scrambled if one was on hand. Though most of my blue light calls were for overdose, really low (or high) BP and sepsis. As well as the occasional unusual condition like an ectopic pregnancy. It's for anything where they can't wait around in an A and E.