Chris F. Inscribed thus:

Actually, the way this circuit is designed, any ripple or pulses in
the DC supply will be picked up and amplified the same way as pulses
from the GM tube. I guess it was never designed to operate on an AC
power supply, but I'm sure there's some way areound the problem.
I've replaced most of the capacitors (all are high voltage ceramics).

Sods Law ! It will be the one that you didn't replace. :-)

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Best Regards:
Baron.