The issue with making steel ingots for the barrel trade was to avoid internal flaws from cooling - shrink cracks. Use of steel was clearly a good thing, but not entirely economical until Whitworth produced ingots that were pressed/forged as they cooled sufficient to prevent shrink cracking. The outside of an ingot cools first and sets the dimensions which the inside must "fill out." As the inside cools and shrinks, it will open up cracks and flaws. By compressing the outside and shrinking the external dimensions during cooling, Whitworth gave the inside a smaller volume to keep filled as the ingot cooled.
JC - the steel trade understood that carbon content controlled the hardness of steel. The trade also understood heat hardening, tempering, and annealing of steels with enough carbon to be subject to heat treating. They did not understand how to make thick pieces without flaws pre Whiworth. Measuring and controlling carbon content and temperatures were the big hitters in steel production, along with mechanically shrinking the outside dimensions as the cast ingot cooled.
Annealing does nothing more than make the steel piece as soft as it will get for the alloy involved. It is accomplished by heating the steel above its critical temperature (exact temperature depends on exact alloy) and cooling it slowly. Rapid cooling (quenching) from above critical temperature will make the piece as hard as it will get, depending on the alloy. Tempering is accoplished by reheating the hard steel to the 500 - 700 F range. This trades a little hardness for a lot of toughness; untempered steel tends to be brittle.
