Strange voltage tracking problem with regulated power supply build
I credit @PlasmaHH with the answer to this problem and his(her?) suggestion that the circuit may be oscillating.  As my updated question shows, the circuit was indeed oscillating and since the oscillation frequency was related to the set point voltage and since my DMM was averaging the oscillation signal, I was getting the weird response.

I wanted to say how I solved the oscillation issue in case someone has the same problem.  Firstly, I checked the feedback loop for stability and in the end I dumped the 680k and 100nF compensation scheme for a simpler 100nF cap between the op amp inverting and output pins.  I also changed the op amp to a NE5532 because I had it on hand and it seemed to reach a higher output voltage before breaking into oscillation.

What I found is that no amount of local compensation would stop the circuit from oscillating eventually, as the output voltage was increased.  But the real winner was adding a 470uF cap at the output.  This is specified in the Farnell circuit diagram but I hadn't added it to my prototype.  It's obvious to me now (but not before) that this is a very important component in maintaining stability.  If I ever get to the end of my Basso book on control systems for power supplies I'll probably understand why.  But, for now it's working!