This looks like a set up in a lab I was involved with where multiple lobbies were installed to control a positive pressure differential between the labs and the rest of the building. It was further complicated by a computer controlled door entry system that in 'working' mode, controlled the door locking mechanisms to ensure the doors wouldn't open until pressures were equalised. (like a canal lock gate).
The local fire safety enforcement team were a bit grumpy as they saw the plans as an inner, inner, inner room and were having little panic attacks which also resulted in a bit of professional deafness - in that they were not interested in the use of the space, any mitigations in place or any other matter. It was a triple inner room and its not happening. They also didnt like that we wouldn't let them in to view the lab for technical reasons
The strategy I compiled looked at the rationale as to why in the fire safety world inner/inner rooms are seen as high risk - ie a fire developing unseen to those in the deepest room. Then I introduced the fact we had AFD in each room and aspirating SD in the false ceiling and raised floor voids, plus overrides on each door-set that would allow escape regardless of the ambient air pressures.
The testing of the AFD was more onerous than BS 5839, we promised (but TBH rarely achieved!) 4 x fire drills per annum and introduced a policy that where detection fails in a lab, it will not be occupied There were three identical labs and the AFD was arranged so each space was on a separate system so a fault in one, wouldn't take all 3 labs out of use. In the very unlikely circumstances that all 3 AFD systems failed, extra staff would be employed as fire watchers for the duration of the use of the one single lab.
So it was my view the MoE was protected adequately my both infrastructure and management systems - and the enforcement team reluctantly agreed
It seems like the biggest difference between my scenario and yours is that we had numerous sterile lobbies with no storage and only lighting, & door entry equipment as ignition sources. So when justifying you gowning area, you may have to show mitigation such as reducing the amount of PPE stored there or the time it is stored there etc.
Good luck
