What's the depth of the nearest valley (within 200m) relative to where you pull water out of?
If there is a valley, it's likely the mine had an adit and it's quite probable the adit is blocked and choked up with "fines". It is also quite possible that during periods of low rainfall, the water dries out to a degree permitting access.
Since it is a small mine, there is a fair probability they were fidding around with old and shallow workings which may point towards having the shafts sunk through workings, or shallow workings which are above the adit.
If it's in a valley floor, or pretty low down, they might have pumped to the surface. Without knowing the area intimately, it is difficult to call. If it was an old mine, it would be interesting to see whether there were any remains where the OS map indicates wells.