The curve noticable on British coaches is sometimes called the tumble-home (which actually refers to the narrowing of a ship's breadth).

The tools required are a vice, something like a Workmate is best, a rule (12 inches is adequate), and a piece of simple profiled skirting board. If you don't have a piece of skirting board which Domestic Authorities will not mind being ripped out then a 0.5 inch diameter metal tube will work, or at a pinch the handle of the brush.

Place the curved former in the vice, and align the coach side with the former, tighten the vice to hold the coach side in place.

Next take the rule and place it next to the coach side, vertically.  Then with your palms, rotate it away from you pressing the WHOLE of the coach side against the former.  The secret is to bend the whole of the side at the same time, with the same pressure applied along the length of rule.  The right hand picture shows me bending a Chowbent coach side, with one hand. This is NOT recommended, I just couldn't use two hands and hold the camera as well!