I know the place well, having been brought up only about 300m from the Wishing Well and was there yesterday visiting my parents.
I think that there is a high liklihood of cave development between the wishing well and Portesham, indeed there is another small spring/rising right next to the junction between the roads leading to Friar Waddon and Coryates. The spring is in a very narrow valley and might repay digging if permission could be gained.
As for the Wishing Well itself, the main rising lies just to the right of the well (looking upstream) and is choked with small stones, though there is the impression of void at times. The rising can be very impressive and regularly chucks out limestone cobbles about 75mm cubed. Any exploration would be va underwater digging, which for years was imossible as there was a trout farm just downstream - that has now gone. However as the well lies in the garden of a cafe I am pretty sure that obtaining permission would be nigh on impossible.
I am led to believe that when the pumping station, about 1 mile away towards Portesham, is operating that the flow from the well immediately drops (I think this suggests that any cave system is Phreatic), but I noted yesterday that the Wey was running very discoloured about 100m downstream of the Well at about 2pm after the rain from Storm Barra in the morning.
Like Tim I have walked pretty much the entire area many times over the last 40 years or so, and there is no obvious place to dig.