Haven't got round to hiring a digger yet but a fair few hours of spadework has uncovered what I think is the source. More by luck than judgement, I found the end of a plastic drainage pipe, about 2' underground. It's metric, so not that old. With my drain rods, I started clearing it but soon came to a hard and impassable blockage, about 3m in.
Some further investigation (digging!) has found a load of old bricks/rubble etc. buried next to the other end of this pipe - I presume someone has filled a pit with rubble to keep it open and then piped the overflow away, although not very far - perhaps it used to reach to the surface?
Have also found an iron pipe leading in a different direction. It's completely blocked (only small diameter, about 20mm) and I've snapped it with the spade anyway. Not sure where that leads to - I suspect it used to lead into a collection tank a little way downstream.
The book (and subsequent conversations with the author) mentioned a large wooden barrel - unless someone has carted another one up there, I dug up a wooden stave!
There are still odd patches of standing water elsewhere in the field so it's probably not the only spring, don't know if I can remedy that without some serious work but at least for now I have a small trickle of clean water. Once I manage to dig down a bit further, I'll sample some.
Oh, also rescued a frog from one of the test pits I'd dug that had filled with water. Released him into the more open bit but don't know if he stayed there or whether the dogs ate him. I've filled the pits in now and left no straight sided traps