Walking like an Englishman

Could someone please explain to me why the English, who drive on the left, prefer to walk on the right? When walking towards someone in Australia, most people instinctively move to the left and allow the other person to pass on their right, as they would drive. In England, expect the opposite. Go figure.

For that matter, where did driving on the left come from? I'm told it goes back to the Middle Ages, where armed men would pass each other on the 'non-sword' side so as to avoid attack. That seems sensible enough. Why then did Europeans and Americans choose the opposite way? Ah, the great questions of existence...