Hello,
Just to the west of Winchfield is an area called Potbridge. I believe that a large portion of it is now under the M3. Potbridge is shown on OS maps but you'll not find it using Google Maps.
On a 1759 map of Hampshire, surveyed by Isaac Taylor, there is a place called 'Pott' (very near a stream - but it's not named) and a stones throw away is 'Baridge Pillers'. So it's not hard to see how the names may have combined and slowly corrupted (or am I just being fanciful?).
However, I've been to the area several times but I've not found a river/stream/brook called 'Pot(t)' - just wondered if anyone had more in-depth local knowledge?
Tim