Thank's. I was wondering initially if it was normal and everyones is like that or I had a problem transformer. I did open it after seeing one of Dave's videos on YouTube, and tightened up the bracket in case it was that. But it didn't seem to make any difference so I put it down to the laminations. I did notice holes in the laminations, presumably mounting holes. Is this where you meant for trying nuts, bolts and washers?
Before I forget, move it to another location directly into the wall as it could be induced noise or line hum etc, turn off mobile phones and fluro lights, tubes, switching supplies etc.
It may have welds so don't tighten too much it's just to see if pressure alters it. If it's welded it means the lamination will have continuity at that spot. The idea is, if you have a bolt running through the lamination you use an insulated sleeve and nylon or fiber type washers as it improves the performance of the transformer.
I should have explained that more clearly, I was actually suggesting making an improvised clamp for the outside of the transformer with a thin bolt, 4 nuts and 2 washers. You can use insulation tape or card stock as a temporary insulator and move the clamp about the transformer if you needed to.
Inserting card between the windings and the core can eliminate another common source of the vibration, just go easy and as I said keep the power off and it unplugged. There is proper insulating card you can buy if you need but I've only ever used it salvaged from switching supplies (not to be confused with RFI/EMI shields).