Our River. I'm not surprised as it strikes me as a good way to get a soaking, but Leslie claims "by using the lee-board when the wind is across the river, a punt sails even better than a rowing boat."
A likely story. I am reminded of Philip Bolger's mystification when people said "that's a nice rowing boat, let's sail her", and that applies to punts with knobs on.
The rig is appealingly simple, however. A loose-footed lug sail with plenty of area high up, needed for water that is mostly sheltered by trees. Steering is done with the pole, and when the wind is abeam the passenger uses a floorboard as a makeshift leeboard.