The photo above - named 'turning out' seems staged.
The order of dressing in my time, 1965 - 1993, was (when wearing normal dress) remove shoes and put on leggings and boots which were kept located together, i.e. leggings on boots, put on helmet and then tunic and axe. Then take your allocated place on the fire appliance - known as a 'machine'.
When I first joined we had a vehicle similar to the following photo but was slightly newer, 1935 in fact and as you were in the open air, rather than in a cab, your sturdy belt was a method of securing yourself to the vehicle. We got a newer vehicle shortly after, a 1955 Dennis.