instructor holding a PPL only cannot be paid (unless they are one of the few left who still have the grandfather rights from the olden days of CAA).
Didn't all those get a honorary BCPL, enabling them to receive money?
Another nugget (not sure if it's true) is that such an instructor, having got his BCPL, now has a "CPL" for the purpose of having an IMC Rating (every UK - not JAA - CPL or ATPL has automatic IMCR privileges) so he can teach the IMCR without ever had any instrument training himself. I am pretty sure I had one such instructor - he had never held more than a PPL.
Instructors can make money - it comes down to utilisation. In Arizona they get to fly 8 hours a day. They could fly 16 hours a day but would be even more knackered than they are already. The problem is the UK weather, and far too few students for the # of schools (or the # of instructors in a given school).