Could be old coppice. Bodgers did strange things in the Chilterns. Was it near High Wycombe?
Yes, the first one was roughly Wendover area, well to the north of High Wycombe, and the second one was roughly Great Missenden area, also north of HW but closer. I thought maybe coppice for the second one, but it's still a bit odd, being linear.
Here's a classic ancient coppice, this one on the escarpment above Princes Risborough which again is north of HW: