Guitars picking up studio buzz from LV transformer

SpankThePlank

Hi folks

I have lately been much more troubled by buzz in my loft studio ever than before. 

I went as far as shielding all my guitar cavities, which helped a little, but recently it was so bad I started investigating further. 

I turned off the striplight, which helped (I know), unplugged various sockets (PSUs, monitors, keyboards - even the computer) whilst listening through the sound card and nothing was getting rid of that horrendous broadband buzz.

It does improve when touching the strings but doesn't go completely, so maybe some odd earthing too.

Then one day to my amazement it was hardly there - this was driving me nuts until I realised it related to the LV transformer above the ceiling (right below my feet!), and the lights were off.

Slight home challenge is I may flail if a family member puts on the lights whilst sensitive, spacious guitar take #56 is going down. This is not ideal for family relations nor winter conditions, so my question is - can the transformer be screened itself? Or is a better transformer less likely to emit the horrible noise? This must be a common issue. I will need to take up the floor to access and I'm not sure resiting it will be that convenient.

Thanks for your electrical knowledge in advance!