Tin foil won't cut it. You might try one of these products, applied to both sides of the partition: (http://www.digikey.com/product-highlights/en/emirfi-absorbers/52080) or (http://www.tweekgeek.com/stillpoints-ers-rfi-killer/)
Tweak or Tin Foil Hat?
I have noticed that my tube amplifier has some noise in it on occasion that seems to be related to my AirPort Extreme wireless router that is in the the same cabinet in the adjacent space. If I get serious about my listening and my wife isn't home I will unplug it, but I have been thinking about using tin foil to make a barrier lining in the cabinet. Any reason to think this might make a difference? I just have not had the time when I think about it to give it a try as of yet.