The in-line combination of a reversing rolling mill (Steckel mill) and its coiler furnaces with accelerated controlled cooling apparatus immediately downstream thereof and associated method permits steel to be sequentially reversingly rolled to achieve an overall reduction of at least about 3:1, imparted by a first reduction while the steel is kept at a temperature above the Tnr by the coiler furnaces so as to preserve an optimum opportunity for controlled recrystallization of the steel after each rolling pass, and a second reduction while the temperature of the steel drops from about the Tnr to about the Ar3. The second reduction is preferably of the order of 2:1 as a result of which the steel reaches a final plate thickness. The steel product then passes through the accelerated controlled cooling apparatus, preferably applying laminar flow cooling at least to the upper surface of the steel passing therethrough so as to reduce the temperature of the steel from about the Ar3 to a temperature at least about 250° C. to about 300° C. or more below the Ar3 at a cooling rate of at about 12° C. to about 20° C. and preferably about 15° C. per second, thereby to achieve a preferred fine-grained predominantly bainite structure affording enhanced strength and toughness in the final steel product.