imho the people at the London proofhouse did know pretty well what they were doing! Since 1895 the Brits used the "Woolwich" or "oiled case system" to determine their "tons per square inch" pressures. In the April 1967 issue of THE AMERICAN RIFLEMAN Roy G. Goodman described this system. The pics are from this article just to save them. Instead of bleeding off some gas through a hole in the barrel to a piston , which in turn deforms a copper crusher (cup) or works on an electronic transducer, the Brits used the cartridge case as the piston. The case worked on a moveable breech, which rested on a copper crusher.

Tons per square inch were then calculated from the force needed to deform the crusher and the base area of the case. The photo shows the "bolthead", the breechblock and crushers new and deformed by various grades of pressure.

The Woolwich system required an oiled cartridge case to preclude friction between cartridge and chamber walls. Using a case and chamber free of oil only gave about two thirds of the "true" pressure readouts. If the case was oiled, case shape had no influence on breech pressure! The pic shows the breechblock and a can of oil in front of the pressure test gun.

The military proof of .303 Lee-Enfields consisted of firing one "blue pill" proofload and one service load with an oiled case. Rifles that stood the proofcharge sometimes failed on the oiled service cartridge. So I think the guys at the London proofhouse know much more about pressures, case shape and oil viscosity than other members of this forum.
BTW, German proofhouses without a proper proof cartridge in a pinch simply heated a service cartridge to 80 degrees Celsius and used this as a "proofload".
2nd BTW, due to even more inertia the Woolwich system gives only about 80% of the pressure readout of the Rodman copper crusher (cup) system. So it is not possible to simply convert "tons per square inch" to cup or psi or bar using a pocket calculator!