Oleg, I have been reseaching the flight-kit again, and I have been speeking with people who have had the pleasure of getting into the spitfire'c cokpit in flying gear, and each has said that it is is impossible for the pilot to wear an Irvin flying jacket. The cramped cockpit would make it impossible for the pilot to get the right-head movement which would be needed in combat.
I hope that this is useful information for you to use. A Hurricane pilot had the luxury of being able to wear an Irvin in the pit, but I would imagine this unlikely during the hot summer.

(also, if the pilot is fitting in the spit perfectly with the Irvin on, does this mean the pilot model is off? This isn't intended for another discussion on pilot size, but more a follow up question on whether layer clothing is modelled. We can see from one video that the parachute is a seperate model)