I found that the Commodore PSU was putting out 5.7V, which I have come to appreciate is too much. To address this problem, I made a "Y" shaped splitter which fed in the 9V from the old Commodore PSU with 5V from a modern Samsung 5V USB charger (which was all that I had to hand at the time). Apparently the 9V is less sensitive to over-voltage so it's OK to use the old PSU for that.
This setup wasn't successful - although the charger was rated at 5V, 1.55A, I found that it's output was closer to 6V (whether under load or not). At first I thought that possibly that I'd demanded too much current from it (the C64 apparently needs 1.5A). So I bought a power supply which has selectable voltages of 4.5V, 5V, 6V etc. The rating is 2.4A at 5V, and the supply did claim to be regulated. It's CE marked and cost about £12, and so I thought it ought to be good enough.
At first this PSU delivered 5.1V onto the main board (as measured at the RAM chips), so I thought my voltage problems were solved. However, after only a few minutes operation I have found that the voltage is back to around 5.7V again!

What is particularly puzzling to me is that the PSU seems to have been permanently affected by it's encounter with the C64. Regardless of whether it is powering the C64 or unplugged from the machine, I find that all the marked voltage settings are delivering more than they did initially - "4.5V" actually gives over 5V, "5V" gives 6V, "6V" gives 7V etc. It definitely didn't do this when I first got it!
Is it plausible that the C64 could have had this effect - and if so, any ideas of what I could do to fix it? I haven't renewed the big electrolytic capacitors on the board yet (I think... it's been such a long time since I last had time to dust off the machine!) so could a fault on these pull too much current and somehow damage a PSU?