AFAIK, the English style are all a rubber pad, covered by a thin layer of leather. The rubber pad is fitted in the normal way, then the sides are faired in about another 1/16" (the thickness of the leather). The leather is stretched on wet, dried, then glued to the rubber pad, the free edge being run over the bottom corner of the pad for a short distance, to give a finished joining edge. Often a thin line is planished in the leather just shy of the joint, just for decoration.The pad is then screwed to the stock, as normal, and rubber plugs, covered with the same leather, fitted in the screw recesses.
Quite a bit more work than just fitting a straight pad, and therefore more expensive to get a nice job done.