Ooh. Looks like a bit of oolite that. Does oolite have any caves?
He is in Stamford - just up the road from me. And yeah, he is on oolitic limestone.
There are subterranean watercourses, some work as been done a little further to the north in the area of the East and West Glen rivers. But nothing anywhere near large enough to get into! Andy Farrant was a contributor to a paper entitled "Groundwater in Jurassic Carbonates" which discusses it in detail.
I highly doubt that Furze will find anything other than cracks in the limestone.
But what perfect geology he has for his project! fractured limestone, and clay at just the right depth for the top of the tunnel!