Africa Special, Part 1 - S19-E6
Corrected entry: Halfway though the episode Clarkson, Hammond and May encounter an impassable river which they cross on a home-made car ferry, dragging it across on stout ropes. The river can't be all that impassable - how did they anchor the ropes to the opposite side before the first crossing? Don't tell me someone swam across - the river is infested with crocodiles.
Correction: Their adventures are always accompanied by well equipped experts and the camera crews. They have the necessary equipment to cross the river, but the challenge was for them to design a way for the three of them to get their cars across. They use the equipment to help them build the solutions. Regardless, on this occasion we see James paddle a small canoe across to secure the ropes.