My understanding is in-order to get the killing performance using steel shot, it requires faster hotter loads.

And what about the pressures? I'm wondering about the chamber pressures for the 1954 London & Birmingham Proof or Re-proof British shotguns?

I had a look in Vic Ventures ‘Gun Craft’, Rules of Proof, pg. 207. In his book, he has a chart from the Birmingham Proof House re: 1925/1954 rules of proof which states, for 12 Gauge, 2 1/2 inch, 3 tons per square inch = 8,943 psi, for 2 3/4 inch = 9,686 psi.

From what I researched online, the CIP “Standard Steel” ammunition pressure limit is 10,733 psi, and the CIP “High Performance Steel” pressure limit is 15,229 psi. So doesn’t the CIP “Standard Steel” ammunition pressure even exceed the 1954 London & Birmingham Rules of Proof? And U.S. SAAMI's specification for 12 gauge, 2 3/4 inch, has a chamber pressure limit of 11,500 psi?

I don’t know, maybe I’m missing something.