Thanks for the replies.
I rebuilt the circuit from scratch - still problems, but slightly different result. I also put filtering caps across pins 21 & 22. Using the external power, the circuit appeared to work - the 5940 felt cold after about 20 secs (when I last checked it). After about 1 min of running the Knight Rider "BasicUse" sketch (I've only got 8 LEDs connected) the LEDs went off, chip was very hot and had blown. Swapped chip, ran sketch for 5 mins plus on +5V from UNO and looks fine.
I dont understand it. I'm now questioning the output of the wall wart and wondering whether there's an issue with this (I did measure the output when I first had the problem, but maybe didn't monitor long enough). If I try and use a 7805 and caps on this power supply the output is 3.9v (wasn't using this on the problem circuit) - I guess because it's because it's only a 5V supply and there's a voltage drop using a 7805. I'm going to find a 9V supply, add the regulator and try again - I'm not that confident, but not sure what else to try.