The question of what to do on an engine failure is certainly part of the U.S. PPL instruction. A turnback is taught as possible above a certain altitude/airspeed and airport configuration but for single engine aircraft unless you have enough altitude/aispeed to assure you make the field the practice is to land more or less straight ahead. As my very gray haired instructor put it with an engine failure on takeoff land into the softest cheapest thing you can see through the windshield.
This was demonstrated to be graphicly one summer day when I watched a light single with 2 adults and 3 children aboard do a textbook stall, spin, smoking hole. He** of a training aid.