Buzz generated by the PSU

Hello everyone.
I'm working on my first class DYI hifi amp.
A "simple" assembly of pre-assembled boards ...let's say a school prototype with no pretensions other than to sound decent. The result isn't top, but I learned many lessons that I hope to apply at best way in V2.
However, there is a very annoying problem for which I would like the valuable opinion: the PSU, I know it is not the best, has two 12v auxiliary outputs. I needed one to power the LEDs on the front panel. Well, if I connect even a single LED to one of the outputs, a constant buzz is generated regardless of the volume setting. With the 12v contacts empty, nothing. I also noticed that if I touch one of the two contacts (under load) with a multimeter tip, the buzz fades out by half or so. The case is made out of wood with no grounding.
Can you help me remove the problem?
 

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Well, I tried connecting the two 0 points of both the output rails to the power supply grounding.
The buzzing has dampened dramatically, didn't fade out completely though.
Perhaps, this residual noise is caused by some frequency