First figure out how much current we're talking about- it's possible it's negligible.
Two possibilities come to my mind.
1) Is the variac in question designed to be used at 240V? It's possible you are saturating the variac core, in which case it will pull heavy current and buzz.
2) If this is not the case, it may just be a coupling issue that can be solved by putting some capacitance across the input "primary" of the variac. If this is the case, I wouldn't worry too much.
I built a very similar power supply for the same purpose, and I put the isolation transformer after the variac. Yes, this means you don't have the fixed output voltages whilst adjusting your variac, but in practice it is rarely necessary.
I would figure out what sort of current we're talking about here. If it's a lot, then you are probably saturating the variac core.